"Cleanup tasks" will always be appreciated I am sure, but again I would caution that there is a trap here. It's easy to clean up any number of things as you go, and construct an illusion that somehow, you are being productive.
When I hire people, aside from fixing mistakes in the documentation they encounter, I want them to have all the time they need to learn, ideally with a set of curated onboarding tasks that progressively give them expertise in the system they are intended to operate in. There is a time to "make things better" and, in my opinion, that's after getting up to speed in a sense that lets me collaborate with the team in a productive manner. I won't begrudge someone the opportunity to clean things up, but each individual is the ultimate arbiter of how to be effective at the end of the day.