Most real estate websites don't offer this because architectural classifications - whether we're talking tax records or what an agent enters on a listing - tend to be really inconsistent and are somewhat general.
Where I live, the classifications don't get as specific as "Victorian" or "mid-century modern". Instead you get "old style" which includes a whole bunch of other stuff that's not even remotely Victorian or in the case of MCM (my personal passion), I've seen everything houses labeled as everything from from "contemporary" to "traditional". Then again, a house built in the 80s or 90s can easily qualify for "contemporary" while sharing very little in common with true MCM style.
Your best bet is to focus on neighborhoods that have a concentration of the sort of housing stock you want. I personally use the Realtor.com app for most of my searching needs.... more