Taking place over thirty years after the end of the conflict, we can say with a fair bit of certainty that there isn't quite that level of preservation of battlefields, but it is important to understand the context of the game here. I've written previously about another aspect of Civil War memory in the game, discussing the post-war presence of Confederate affiliated criminal groups, which strictly speaking also isn't accurate that long after the war (although in-game lore makes clear they haven't existed the entire 30 years, but rather are a recent resurgence). But what both of these elements point to, as well as other inclusions in the game, is a heavy lean in on common tropes of the Western, as many classic films, on which RDR2 is of course drawing inspiration from, use the Civil War or else its immediate aftermath as part of the backdrop against which their stories are set. The presence of a battlefield, still strewn with debris and while overgrown, done so in a way that suggests a few years have passed rather than a few decades, doesn't reflect reality of 1899, but it does reflect popular media. For me at least, it was quite hard not to think of the scene from The Good, The Bad, and the Ugly where we come across the aftermath of a battle, and I'd hardly be surprised if that wasn't a direct inspiration, as it feels intentional.
Now, while it might not look exactly real, we can discuss the state of battlefields in the period. As already noted, the ones in the game are well kept all in all, and while this is not too far removed from the period when battlefield preservation began, they certainly didn't want to keep them in that sort of state. Early battlefield preservation was mostly focused on memorialization of the dead. Many battlefields had national cemeteries created on their grounds, or else nearby, where the Federal government interred the Union dead. Fredericksburg National Cemetery for instance was founded in 1865, Shiloh National Cemetery in 1866, and Gettysburg National Cemetery was created before the war even ended, in late 1863. Confederate dead were not placed in Federal cemeteries, but some of the earliest Confederate groups to form in the post-war were the Ladies' Memorial Associations who saw to the internment and maintenance of the cemeteries and memorials for the fallen traitors.
By the turn of the century, the battlefields themselves were beginning to be preserved as historical sites. This movement began in the 1890s, first with Chickamauga and Chattanooga National Military Park in 1890 and soon followed by Antietam National Battlefield was also in 1890. The process continued on for decades. Even before their official memorialization, many former battlefields were serving as grounds for reunions of veterans, and many battlefields were preserved by local veterans or memorial groups, such as the UCV, SCV, or UDC. This impulse especially came to the forefront in the 1890s as the preservation of such 'sacred ground' was seen as an important part of keeping alive the flame of the 'Lost Cause' that such groups in the South worked to perpetuate.
To be sure, some battlefields never saw significant efforts at preservation, but far from meaning they were left alone, more often than not that meant they became farmland again. Civilians needed to get back to their lives, and anything too broken for the armies to haul away with them, they would need to deal with instead, which could mean months of backbreaking labor by communities simply to reclaim their land for use again.
Even battles in forested areas, by 30 years onwards, often had seen those woods cleared for more farmland. And whatever the preservation state 30 years on, in the immediate aftermath, the most accessible detritus would long have disappeared. Battles were rarely fought far from settlement, and this certainly isn't the case in the game. After the armies left, civilian populations would scour the field and recover things they thought useful, and as noted, haul away anything simply in the way.
The military too, of course, would scour the field to remove the dead and such, a thoroughly distasteful job often forced upon the African-Americans supporting the armies, regardless of the side. At many battles, the dead were buried where they fell at first, and only later would parties come to rebury them properly, although there would of course be remains in the open that were missed. The remains were often buried under a few inches of soil, civilians commenting on the abhorrent stench that would remain for months. Quite literally buried where they lay, this often meant more work for the civilians who had to remove the bodies and rebury them elsewhere, not only to make their fields usable, but often because of makeshift graves literally on the doorstep or under their porch. Only wealthy officers would usually have the luxury of being shipped home to rest with their loved ones.
Even preserved battlefields have tons of material though! It just isn't out in the open like that. Trenchlines are often preserved, but natural erosion and weather means that they don't look as sharp, and wood elements such as the duckboards would long ago have rotted of course. Plenty of weapons are left behind, but by 30 years on, most would be buried, and require excavation to reveal. Even the best preserved battlefields occasionally have new finds of material that wasn't recovered the first time around. It is perhaps ironic that the closest thing you might find to ignoring such matters would be in the North. Few major engagements took place there, of course, but for the ones that did, while there was great concern about preserving the Northern honor, less attention was paid to the South there. At Antietam, for instance, while the Union dead were moved to the cemetery quickly, Confederate dead, buried on the battlefield itself, were mostly not dealt with for another decade, finally unburied in the 1870s, although not placed in the National Cemetery of course.
But in any case, to return to the original point, by 1899, many battlefields were well on their way to preservation as National Military Parks, and even those which didn't receive such treatment were hardly abandoned immediately after the battle to never be handled again. Even the small engagements saw efforts to clear up and memorialize the dead, and it is quite unreasonable to consider the representation of a former battlefield in RDR2 as close to reality. But it shouldn't be understood on those terms in any case, but rather understood for the Western tropes that it represents and the important place Civil War Memory has long held in the genre.
Sources
Adams, Michael CC. Living hell: The dark side of the Civil War. JHU Press, 2014.
Cashin, Joan E., ed. War Matters: Material Culture in the Civil War Era. Chapel Hill: University of North Carolina Press, 2018.
Janney, Caroline E.. Burying the Dead but Not the Past: Ladies' Memorial Associations and the Lost Cause. University of North Carolina Press, Jan 2008.
Sellars, Richard West. Pilgrim places: Civil War battlefields, historic preservation, and America's first national military parks, 1863-1900. Vol. 3. Fort Washington, PA.: Eastern National, 2005.
Slotkin, Richard. Gunfighter Nation: The Myth of the Frontier in Twentieth-Century America. University of Oklahoma Press, Dec 1992.
Stone, Richard D, and Mary M Graham. 2007. “Selective Civil War Battlefield Preservation as a Method of Marketing The Southern ‘Lost Cause.’” In Conference on Historical Analysis & Research in Marketing, 221–27. Durham, NC.
Sutton, Robert K. "Commemorating the American Civil War in NAtional PArk Service battlefields" in The heritage of war. Gegner, Martin, and Bart Ziino, eds., Routledge, 2011.
I haven't played RDH2 so I dont know exactly how the scene looked but I think I can help with your question.
The answer to your question is both no and yes. So I will break down the three specific subjects you referenced in your query.
Cannons, small arms, tentage, equipage and the material remains of war were usually gone within days of the battle, either for reuse if the condition is still fair or better or re purposed if possible by either the military or locals. This can be seen by the many reports and stories of the Confederate army reusing everything they can from the Union army from small arms (Springfield and Prussian made Potsdams specifically which the Confederate army did not have access to), to uniform pieces which led to some confusion over the appearance of A.P. Hill's men at Antietam, to accouterments like knapsacks and tents that were easy to pick up and use if the soldier needed one.
There was also the habit of relic picking at battlefields by civilians. This occurred at nearly every major and some minor battlefields. This led to later relic boards being made and being quite common, like this. This was also done by the veterans themselves. Some of these relic boards are filled with very unique pieces and can occasionally be found for sale on eBay or through online auction houses. They generally are more destructive to the original items through use of screws through the actual item to hold it to the board.
We can even see at such an event like the 1888 25th anniversary of the battle of Gettysburg where large numbers of veterans and civilians alike turned out to the battlefield where many monuments were placed but not people tripping over relics of the battle. This NPS. write up on the 1888 reunion shows multiple photos of the battlefield around the monuments at that time.
Trenches and earthworks are another story. Many of them still exist today. you just have to know what you are looking for in order to tell the difference between a naturally occurring hill or depression and the remains of a trench. These can be seen easily at places like Spotsylvania, North Anna, Cold Harbor, Petersburg and even in South Carolina at small skirmish sites from Sherman's Campaign of the Carolinas. A quick google image search can give you thousands of examples of earthworks that have survived.
By barricades I am assuming you mean like fences, felled trees, and the like. No these did not survive, at larger battlefields that took days to recover from they were usually gone within days of the battle being used for fire wood. At smaller battlefields they would rot and decay if not reused or burned.
Hope this helps.