Many apps where every user has his own data, which just needs to be synced between devices.

I think I missed where writing to the database precludes backend logic. Databases have triggers and integrity rules, but beyond that, why can't logic execute after data is written to a database?

Writing directly to Firebase is rarely done past the MVP stage. Normally it's the reading which is done directly from the client. Generally writes are bounced through Cloud Functions or a traditional server of some form. Some also "fan out" data, where a user has a private area to write to (say a list of tweets) then they get "fanned out" to follower's timelines via an async backend process which does any verification / cleansing as needed.

It's a really good question

context: I have a near-100% naive perspective. Mobile dev whose built out something approximating Perplexity on Supabase. I have to use edge functions for ex. CORS, but by and large, logic is all in the app.

Probably because the client is in Flutter, and thus multiplatform & web in one, I see manipulating the input on both the client and server as code duplication and error prone.

I think if I was writing separate native apps, I'd push everything through edge functions, approximating your point: better to have that sensitive logic of what exactly is committed to the DB in one place.