Such as? Only one that comes to mind is ESPHome, and I run that separately just fine.

NodeRED is a complete PITA to set up outside of supervisor. It requires extensions on both ends, and it passes the auth in a weird way.

I'm running NodeRED and ESPHome in their own docker containers, integrated with home assistant, just fine. Never used supervisor. It's been a few years since I set them up so I don't remember the details but that also means it wasn't anything notable. They've been stable since.

Do you have it embedded in the Home Assistant UI, and using HA user credentials?

I have HA install in container for a few years - not sure what's "critical addon". Some are helpful, but they're easy to run independently.