It depends if we're talking about him just snapping back to life, or somehow still being alive all this time.
If he's just 160 years old and has lived through the last 100 years, I think he would have stayed a Democrat the whole time and adjusted his social views accordingly. But if 1925 Bryan were reanimated in November 2020, yeah, he's going to have no concept of anything going on. I think he would have a strong dislike for Trump still though.
This is a great answer, and your first question is an absolute must for these hypotheticals, IMO. Look no further than Bill Clinton, who was campaigning for President as a Democrat with a Confederate flag prominently displayed in 1992 and pretty much just tows the party line on social/cultural issues in 2023 ... "being a Democrat," it turns out, was a stronger aspect of his personality than anything to do with the Confederate flag, that flag was just simply more associated with a Democrat from Arkansas without controversy in 1992 than it is now.
On that same note, being a fundamentalist Christian from a rural area wasn't some no-go for WJB as a Democrat when he was alive, and it's not like part of his campaign
against his Republican opponents had to do with his "socially conservative" views; he was very clearly focused on income inequality and proper (in his mind) regulation of corporations. As you said, I think there is a bit more of a discussion to be had if a man of his era was just plopped down into 2020 and heard about things like transgender rights and whatnot for the first time, but I have little doubt that if he simply lived through each decade and never died, his economic views would remain the most important part of his philosophy. And I think that would mean he's still a Democrat.