Sengoku Jidai 2.0 ; how was the geopolitical context of Japan after the fall of Tokugawa Shogunate different compared to the fall of Ashikaga Shogunate, and why did it peacefully transmit to the Meiji period without a large scale civil war like the Sengoku Jidai of the 16th century?

As /u/kumbhira pointed out, the Meiji Restoration was not exactly peaceful.

However, it indeed did not fall into many decades of civil war.

I wrote here about some of the ways the Edo Bakufu (Tokugawa Shogunate) differ from the Muromachi Bakufu (Ashikaga Shogunate) and some of the ways the Edo Bakufu kept the peace. This is surely important to the discussion. The domains having for so long been too weak to challenge the Edo Bakufu, and Japan being much more centralized than during Muromachi Bakufu, when the Shōgun in a way had to rule by consensus and was only the first among equals, that the domains in the 19th century were more willing to follow whatever the central government ordered, whoever that central government was.

It's important to identify that both the cause and result of the change was completely different. The Sengoku broke out when the Shōgun proved uninterested in/unable to quell a bunch of regional conflicts, and instead the people participating in those conflicts, due to politics, ended up on different sides of a central conflict. Before even the outbreak of the Ōnin War, local conflicts had been raging for over a decade without end. While there were large riots in the Bakumatsu (the period prior to and of the Meiji restoration) like the Mito riots, there was nothing on the size and scale of the Kyōtoku War or the Hatakeyama succession crisis. Both began in 1454 with no end in sight, and both, especially the latter, were significant causes to the Ōnin War.

Also an important point is that in the Ōnin War and (most of the) Sengoku, the legitimacy of the Muromachi Bakufu and its right to rule was never in doubt. Indeed, because it was never in doubt, people fought long and hard over control of the Bakufu. That by their fighting the Bakufu was less and less able to keep the peace over Japan was irrelevant to the participants, but the end result was that as there was no central authority capable of militarily enforcing a rule, locals will settle their many conflicts by themselves, which means by force if necessarily.

In contrast, in the Meiji Restoration, not only was the fighting over the Bakufu's right to exist, there's seemingly was no doubt that the Bakufu was over. The Bakufu has always ruled in the name of the emperor, and if the emperor was going to give the right to rule to someone else, well then the Bakufu no longer had legitimacy. Ironically, the Bakufu played a role in this by importing Confucianism as its ruling philosophy, and Confucianism held the rule of the emperor and loyalty to him as highly important. Importantly, although it resisted for a time, the Edo Bakufu seemingly came to recognize the eventuality and the Shōgun formally disbanded the Bakufu "gave power back to the emperor" in 1867. The fighting in 1868 was essentially over who was in charge of the new government, the ex-Bakufu guys or the new kids on the block. Since the Bakufu was not willing to challenge the legitimacy of the emperor's "direct rule", whatever the emperor said goes, and the emperor declared for Satsuma and Chōshū. This decided the battle of Toba-Fushimi, and so basically decided the Boshin War.

Finally, the fact of the matter is that the government transition and the fighting was so decisive, with the Boshin War basically decided in a single battle and lasted only a year and a half most of which was mop-up. The fighting had barely begun and the ex-Bakufu forces had basically only lost a single major battle, before the ex-Shōgun gave himself up and went under voluntary house-arrest, and Edo Castle surrendered to the new government. There was simply no time for local powers to become independent, for resentment to the center to rise, and for the central government, whoever it may be, to lose control of the countryside. In stark contrast, not only were there already widespread local conflicts prior to the Sengoku (if we don't use an expanded date), decades of indecisive conflict both at the local level and at the center fueled resentment of locals for being called to war year after year with nothing to show for it, further fueling unrest in the countryside and forcing locals to take matters into their own hands.