I last applied this approach a few years ago at an IIOT startup, where we had billions of rows of sensor data. We needed it all in one place, but with a fairly varied set of users, like an application team showing customers various slices of their data and a data science team applying all kinds of analytics to the data.
When I showed up we had a single Postgres database with a half-dozen different clients. One managed the migrations in addition to doing real work, and the others were a mix of "direct" users and API layers used elsewhere. Tons of overlap, tons of repeated logic, tons of inconsistency.
I used this approach to first stem the plague of direct DB access, and later to consolidate our APIs. It worked pretty well, and the folks I left it to seemed to appreciate my approach.
We did have a lot of debates about what is or isn't "business logic", what belongs in this DB or not. We tried to keep it pretty light; our raw data was many independent tables, and our API schema had functions for insertions and views to make that data usable in ways that didn't feel very application-specific.
I was pushing to replace our handwritten API service(s) with something like Hasura, though that didnt happen before I left. I think that's where this approach gets more powerful: manage your data with your database, get a web API for free. Then your data store is encapsulated behind a singular service with a well-defined API.
You're right that it requires some serious attention to the DB. We wrote all migrations in PL/pgSQL (managed with sqitch), giving us a level of control that is hard to get from a language-specific migration framework. That required a lot of upskilling, but I think it was worth it for us.