I have just begun encountering this for one of my clients. Their current data lake is azure synapse. For some hyper-secure data, they recently stood up a new serverless instance. Connecting to that instance via data adapters has worked fine, but when I tried to make my normal connector, it hit this same error.
Running sql profiler on a local lab, I can see that the typical call (using BRApi.Database.ExecuteSql) wraps the sql in NO_BROWSETABLE OFF/ON set statements. Apparently this is not supported for the serverless, so it was failing.
My workaround has been to set up a parameterized data adapter to support the desired integration query. Then I'm fetching it as a dataset instead of a dataadapter (BRApi.Dashboards.Process.GetAdoDataSetForAdapter).
One other wrinkle we just encountered, the pure existence of this external connection seems to have broken our table data manager dashboard. I was able to fix part of this, but it still fails on some of the pages. Very frustrating since I have no apparent control over this property SET...