Seems reasonable and thank you for soliciting my input. You're the expert with tab-bar, I'm just a happy minor contributor. I do have activities/tab-bar UI features I use and don't want to break. Relevant to this particular discussion, I rely on activities-tabs face to visually differentiate activities-controlled tabs (I put a one-pixel box around the tab).
I do similar things for tabs under other control regimes and have customized formatters for groups and tabs for both colors and content (prefixes for group names, prefixes for tab names that have "project" buffers). And lots of customization around general usage; e.g., you know about the work I did on optionally collapsing tab group members (Emacs 31!).
-S