It looks like CodeIgniter uses lots of global variables.
https://codeigniter.com/user_guide/general/common_functions.html
I'm not a Laravel dev, but I'm assuming that as a relatively modern framework, Laravel does not rely on many globals by default. So I suppose there's more opportunity for conflict, but only if someone is abusing Laravel.
(Laravel people: Feel free to correct me on this.)
Regarding PHP 8: CodeIgniter has at least passed this guy's smoke test on PHP 8.
https://forum.codeigniter.com/thread-78091.html
Since minor versions theoretically don't contain breaking changes, you may find success on 8.1 as well.
Regarding sessions: I know nothing about how either framework handles sessions, so I can't speak to this.
As for whether it's a good idea: I'm not sure I fully understand what you're trying to do. Are you going to have a CodeIgniter project running side-by-side with a Laravel project, using a separate subdomain for each? Or are you going to try to make the existing CodeIgniter project live inside of a Laravel directory structure, as the title of the question currently implies?
If the latter, I would say you're in for some tears. It sounds very painful. The former could work pretty well, I would imagine, especially if you're already using your PHP mainly to serve API endpoints and can just gradually move all the endpoints over to the new platform, one at a time.
I hope this helps.