Looked through the FAQ but couldn't find anything on this precise view.
Hiya!
I'm certainly not a specialist on the US Civil War, and I've no doubt others would have a great deal of insight to provide here. Having said that, I have done a deal of research and some essay work on essentially this exact question, albeit a long time ago. What I'm sharing here is a re-working of the ideas in that essay, - with the benefit of a great deal of experience and learning! Alongside the discussion below, I've also tackled the idea of the Civil War as a 'total' war. However, with far more knowledge and a little more wisdom, I feel I'd need to rework and re-examine my arguments and conclusions before providing a discussion of total war - I'm no Civil War specialist, and I feel work at the time could have been more rigorous! I'll nonetheless elaborate on the Civil War's 'Totality' if you like, though it may take a little more time.
Moving on, the Civil War as a 'modern' war. Really, to try and characterise the Civil War as a ‘Modern War’ or some sort of ‘non-Modern War’ is essentially a false dichotomy. What we call modern war is, by nature, a relative term. Compared to the ‘modern’ wars of the 21st century, the Civil War is obviously unrecognisable – lacking extensive mechanisation, aircraft, automatic weapons, and fundamentally different in nature and scale. Since it would be absurd to examine the Civil War by the standards of truly ‘Modern’ conflicts, we need to redefine what is meant by ‘Modern War’. The most useful comparisons to make – at least in my opinion - are those of the major conventional wars of the second half of the 19th century and first half of the 20th century - namely the Franco-Prussian War and the two World Wars. In this context, the Civil War represents neither a ‘Napoleonic’ nor a ‘Modern’ style war, but rather a transition from the former to the latter. I've broken down the similarities and differences which the Civil War had to these wars into four sections - technology, strategy, logistics & medicine and command structure.
The Civil War saw the introduction and implementation of a number of technologies that would end up being important, and even central, to the great conflicts of the 20th Century, but in many cases, these technologies were used inefficiently or ineffectively – ultimately, they would have a marginalised impact on the war itself. Excluding Rail (which I’ll talk about later under Logistics), the greatest of these advances was the application of the telegraph and creation of dedicated signals corps for military use. Pioneered by the Union under Albert J Myer and instituted in all Union armies by 1864,^1 the U.S Army Signals Corp saw the massive increase in the speed of communication between Union armies – an innovation that would be emulated by all major European powers, and central to Prussian strategy in the Franco-Prussian War.^2 Another influential development was the Ironclad, which represented a huge leap in naval warfare, rendering Napoleonic era ships-of-the-line obsolete and resulting in combat more akin to the naval engagements of the First World War – but ironclad technology was well-and-truly established, and far more advanced in Europe.^3 The models employed in the US Civil War were extremely basic compared to those already produced by the European Great Powers, and ultimately contributed little to the development of naval military technology.
Ultimately, many of the technologies that would be so critical to the Franco-Prussian War and later conflicts were entirely absent in the Civil War, which to me is indicative of its nature as a war of transition. Noticeably, both the Union and the Confederacy relied entirely on muzzle-loaded cannons and musketry, while their Western-European counterparts were already converting to breach-loading rifles and, in Prussia’s case, breach-loading artillery. Machineguns, while present in the final stages of the war, appeared in negligibly small numbers, meaning they realised little of the massive impact they would have on 20th century warfare.
Strategy
The military strategies employed by both sides during the Civil War once again show a blend of conventional Napoleonic style warfare with the ‘Modern’ warfare of the 20th century. Particularly in the early war period, both the Union and the Confederacy practiced Napoleonic style force movements and military strategies. Both forces operated in long columns and concentrated their armies into line formations for battles. Having said that, we can certainly see considerable military innovation throughout the Civil War that was in some cases comparable to conditions on the Western Front in 1915-1916 - around Vicksburg in 1863 and the Siege of Petersburg in 1864-5, where both sides made very heavy use of Trench-Warfare and fortifications. At Petersburg, a stalemate developed from October 1864-March 1865, during which the Confederates developed an effective doctrine of Trench Warfare, which were highly successful in fending off Union assaults.
Logistics and Medicine
Developments in Logistics distinguished the American Civil War from earlier conflicts and formed the foundation for the logistics systems of the Franco-Prussian War and World War One. The use of rail in supporting military formations with supplies proved vastly more effective than traditional wagon-trains employed in previous wars. Logistical requirements for forces had increased between the Napoleonic wars and the Civil War, as armies reformed to become less reliant on scavenge for resupply.^4 Confederate forces attempted to maintain a supply standard of 33 wagons per 1,000 men (dropping to roughly 26 by the end of the war) compared with Napoleon’s Grand Armée standard of 10 per 1,000 men,^5 resulting in a greatly reduced need to forage. The use of rail to move supplies closer to the front line aided these efforts greatly, being faster, more effective and more efficient than long wagon trains, while freeing up animals and men for the use in other positions. Rail was also used to multiple instances, particularly by the Union, to rapidly transport men to the front. As an example of this in action, the ability of rail to move large forces proved decisive for the Confederacy at the First battle of Bull Run, where 12,000 reinforcements were rushed from the Shenandoah Valley, turning the tide of battle.^6 While the Confederacy lacked the logistics and industry to make full use of rail throughout the war, this approach of rapid mobilisation along rail-lines became a cornerstone of European mobilisation strategies for the First World War.
While medical practices during the Civil War were in many ways similar to those of the Napoleonic Wars, the organisation and formalisation of medical practice within the Union and Confederacy led to the system of casualty treatment instituted and refined during the World Wars.^7 In particular, the Civil War saw the development of detailed record-keeping systems within both armies, which aided further developments and studies into wound and infection treatment.^8 The high casualty rates of Civil War battles and poor medical response during the early war period^9 also resulted in the development of an effective triage and casualty clearing system by both sides, which would be emulated to a considerable extent by European powers during late conflicts.
Command and Administration
Finally, the Civil War saw the transition from decentralised, departmentalised command structures to more ‘Modern’ military commands – however, these changes came during the mid-late war period. At the onset of war, both the Union and the Confederacy had unclear and inefficient chains of command, resulting in miscommunication and competition. The Union, aided by its extensive telegraph network, which allowed the centralisation of information, was first to address this failure, instituting a General Staff system under Grant in 1863. The Confederacy, however, failed to adapt as effectively, only formalising the same system properly under Robert E. Lee in early 1864. Prior to this time, it relied on a Departmental command structure, which resulted in serious logistical and strategic inefficiencies. This was another of those areas where European practices were considerably more refined than those of the warring US states, and to an extent Union and Confederate forces found themselves re-inventing the wheel.
In summary: The Civil War was a very complex, constantly evolving conflict that saw a wide range of strategies and circumstances, and saw a major transition phase between ‘Napoleonic’ warfare and ‘Modern’, industrialised warfare. To classify it with binary terms such as ‘Total’, ‘Modern’, ‘Limited’ or ‘Primitive’ oversimplifies the diverse reality of the war. Touching on total war, the Civil War saw the extensive mobilisation and modification of civilian industry and society to aid the war effort in the South, but only to a small extent in the North. It saw the use of Scorched Earth policies, the targeting of civilians and civilian assets, but also respect for civilians and exclusion of civilian targets under some circumstances. Similarly, the Civil War saw the extensive use of both ‘Napoleonic’ and ‘Modern’ technologies, strategies and policies, adapting to the realities of warfare and transitioning from the former to the latter. Ultimately, the Civil War would exhibit developments in strategic thinking for future conflicts, debuting ideas and technologies that would play a central role in the calamitous conflicts that would rock the world throughout the 20th century.
This is definitely only one aspect of the answer, but some historians see it as precedent of "total war" and specifically single out Sherman's "March to the Sea". His plan for this operation was to not only beat the enemy's troops in traditional field combat, but also to destroy what could be used as the building blocks of renewed resistance / guerilla warfare even after a formal military victory. In practice, this meant foraging the most productive agricultural strips of land in enemy territory (so partly having his own troops feed off the land) and destroying buildings and infrastructure (including railroad tracks and bridges) along the way. This is sometimes seen as an early example of total warfare and "scorched earth" tactics like those used in the World Wars (especially WW2, Eastern Front).
If you use this as an important feature of what a "modern war" is, the case for the Civil War being the first is there.