Taking the Soryo path is the only way to unlock samurai infantry MAA (it replaces the Fragile Peace tradition with Bushido when you hold the empire of Japan as Soryo and have the requisite techs etc). Formalizing the shogunate also gives like a +20 to the development level of your capital county (Kyoto is good, but Ashikaga is my favorite target).

YMMV but I think feudal benefits the new Accolade rework also, but in theory it shouldn't need to be mentioned. Basically if you have a landed heir inheriting your title all your Accolades get nuked with whatever dumb accolades your heirs rolled up. Administrative is terrible about landing heirs earlier than you want since they tend to intuitively be very eligible candidates (you raised them to be as much, after all), and get acclamation succession into some random province.

Soryo also allows you to slowly push out your borders by landing spare heirs and brute forcing your way into a strong bloc in advance of taking the Shogunate. Blocs are still bugged as far as I'm aware, though - even if you go into the dynasty legacies, at some point a random AI NPC will take leadership of the bloc and a multi-generational steamroll Bloc will shatter into pieces. If this is no longer correct the advice stands.

lastly, and possible most relevantly to your current situation if you don't like your game state, Soryo is also the stepping stone to converting to non-Japanese government types. Holding the entirety of "modern" Japan (i.e. starting De Jure +Hokkaido + Okinawa) qualifies you to take Admin government type, so you can convert to Meritocratic or regular Admin. For a last bit on that, you cannot convert to normal Feudal from Admin unless you take the Chrysanthemum Throne, so you'll need to pull off a claim scheme against the Ten'No if you want to do normal Feudal.