Does immutability mean something like ChromeOS, where you cannot install packages on the system itself, but you can create containers on which you can freely install software, including GUI?

If yes, what are some good options for someone looking for a replacement to ChromeOS Flex on an old but decent laptop?

Yes, that's exactly what immutable means for Linux distros. Sometimes they're also called atomic for mostly the same reasons.

I don't have good experiences with snap and flatpak, so I hope this is not it.