This same question gets asked regularly:
- Update "HA Core" or "HA OS" First? Both show needing updates
- Updating home assistant, which should I update first?
- OS, Supervisor, Core - update order?
Strongly-related questions also get asked, e.g.:
- Supervisor, Home Assistant Core and Operating System Updates
- Updating OS, Supervisor and Home Assistant Core
Suggestion: when HA UI shows that Core and OS updates are both available, it should also recommending which order to update them in - or even better, provide a button the user can press to apply both updates in the best sequence.
This would avoid user stress and duplicate questions.