There is a 19th Century view of the Presidency that needs to be covered. The Presidency was not a particularly strong office at the time. It was not the driver of domestic policy. That was generally driven in Congress. President Buchanan's view was that the President was just the person responsible for executing the domestic policies as defined by Congress as determined to be legal by the judicial system. His background was more related to foreign affairs and that was the one area a 19th century President was responsible for. He managed to avoid the domestic crisis on the Kansas-Nebraska Act by being out of the country as an ambassador to Great Britain.
He had hoped that the Fugitive Slave Act and Kansas-Nebraska Acts combined with the Dred Scott decision would have settled the sectional tensions, so he could concentrate on his foreign policy objectives. But, domestic issues were front and center.
Buchanan had a remarkably legalistic approach and viewpoint. He felt it was his duty to execute the laws of the United States. He didn't ever seem to grasp the moralistic opposition to slavery and tended to sympathize with the pro-slavery position because he saw slavery as legal and enslaved people as property. He felt that abolitionists were undermining personal property rights.
That said, he also upheld the treaties with the UK that made the African slave trade illegal. He scrupulously upheld the United States obligations to return Africans seized on slave ships, even when he privately complained about those obligations and the expenses associated with them.
First, he supported the pro-slavery side in the Kansas. That lead to a great deal of animosity and he had no effective answer to that violence. It was up to Congress to decide on what terms would be acceptable for Kansas statehood and Congress was hopelessly blocked on the slavery question.
When Utah became an issue defying United States authority, Buchanan acted decisively, send a new administration and army to quell any thoughts of independence by the Mormons in Utah.
As both Kansas-Nebraska and Utah were federal territories and not states, tgey fell under federal authority, so he could deploy troops there to deal with tge violence. However, the use of federal troops in states was strictly limited be law.
When everything came to a head in 1860, it was President Buchanan's strict legal approach that exasperated the situation.
He felt that the southern secession movement was illegal. He believed that the constitution did not allow for this action. This became an issue when South Carolina seceded. He considered their actions illegal, but it had not been addressed in court. In the absence of that, he felt that Congress was the body to determine the legality of secession. Until then, he was obligated to operate under existing laws and responsibilities.
The primary law at the time relating to that was the 1807 Insurrection Act. That act specified that cases where the federal government could use troops to put down an Insurrection. The specific cases, however, did not include the variation of a state government rebelling against the federal government. So, Buchanan did not believe he had the legal right to use federal troops to intervene in the secession question.
He did, however, believe he was legally responsible for the property of the United States. The South Carolina government had seized United States property and that was blatantly illegal from President Buchanan's perspective. And, when other states followed suit, it became a very large sticking point in terms of even basic negotiations.
South Carolina sent an emissary to negotiate for the purchase of Fort Sumter. President Buchanan was willing to listen to the position of the South Carolina emissary Isaac Hayne, but the SC government had misread President Buchanan and his approach. They asked for him to recognize them as a sovereign nation and settle on a sale price. He refused the recognition as he felt that secession was illegal. He refused to sell any US property as that needed Congressional approval, which was not forthcoming.
He did arrange a truce with the states of Florida and South Carolina to cool things down as they were rapidly moving towards an open war in January 1861. He supported reinforcing US installations where feasible. He tasked the war department with determining options.
He was very angry when General David Twiggs surrendered the US forces and property in Texas. He considered Twiggs to be a traitor.
Buchanan actually did quite a deal in areas where he believed he had the legal right to do so. He supported calling up the DC militia and purged it of disloyal members. He called back the navy and supported the fleet deployments off Forts Sumter and Pickens.
A personal observation: President Buchanan stated his position clearly and repeatedly in every instance I can find. In terms of secession, his private communications and public statements match in every aspect. He did nothing underhanded and appears to have no hidden agendas. He was simply put in a position where he would have to break the law to support one side or the other. He could not, as President, recognize the seceded states as sovereign or release US properties to them. He could not, as President, call on federal troops for a domestic issue inside existing states.
Basically, the Southerners originally thought he would support them as he was sympathetic to their core complaints and found out the hard way that he was very much the President of the United States and he would not commit treason or break the law on their behalf.
The pro-Union side had hoped he would quell the secession movement by recalling the army, but he had no legal grounds to do so and the army was too small to have managed that task.