Clearing up some junk memory. CleanMyMac? (and TimeMachine)

I would strongly advise against installing CleanMyMac, as it's almost certainly going to create issues.

I would also advise you to review this Apple Support article prior to letting your old Mac go: What to do before you sell, give away, trade in, or recycle your Mac - Apple Support

Failure to perform the steps in the above link could well result in your old Mac being nothing more than a "brick" for the new user...or preventing you from being able to properly set up your new Mac when you get it.

Hope this helps.

I concur with the previous two posters. CMM is a horrific product. Although this article touches on a number of things that you haven't asked about, it also talks about products like CMM:

Effective defenses against malware and ot… - Apple Community

CMM is a disaster for Macs; it does nothing at best but can make matters worse via system disruptions.

Time Machine backs up your full dataset, but not the OS.