I would start by using Softaculous to remove all applications that it knows about. That will at least remove a lot of stuff and leave you consistent with what Softaculous (or whatever one-button installer is on your server) thinks you have. Note that LP is going around and forcing applications not installed through Softaculous into that system, so they can be forcibly updated. If you clean out old installations manually (after letting Softaculous do its thing), but before LP plays with your site, it should probably stay consistent. Be sure to have an offsite backup on your PC!
Then you can manually remove old backups and data files not related to applications. If you don't know what it is, and it's in your account root directory (above public_html), I would suggest leaving it alone, in case it's some important system file. In public_html, leave the .htaccess (go in it and clean out anything that seems to be application-related, such as SEO, but leave anything that forces https or forces www/non-www, sets error handler pages, etc.). There may be cgi-bin, scgi-bin, ftp, and other system directories at public_html -- you can go in and clean out anything you recognize as something you put there, but there may be some stuff put there by the system. .well-known is for your SSL and should be left alone. If you don't know what it is, you can usually leave it alone unless you find it's causing problems. Obviously, application-related directories and their contents can be removed if you wish.
You may not end up with something as absolutely clean as a new account, but at least you can clean out the bulk of it. As a general rule of thumb, leave a file or directory alone if you don't recognize what it is or where it came from. Maybe you could ask LP if they can reset your account to "brand new" content, but they may charge you for the service. They may be willing to tell you if they put certain files there, if you give them a short list. If you have stuff like error handler pages or Google identifier files, you can usually leave them alone.