Adobe's caches are larger than the applications, and there are four

Creative software is generous with disk in a way that is mostly defensible: caches make a timeline scrub smoothly and previews make a large document open instantly. What is not defensible is that almost none of it is cleared when a project ends.

The four kinds, and where they are

du -sh ~/Library/Application\ Support/Adobe/* 2>/dev/null | sort -h | tail -10
du -sh ~/Library/Caches/Adobe* ~/Documents/Adobe* 2>/dev/null | sort -h

The media cache is the big one

Premiere and After Effects write conformed audio and peak files for every clip they touch, and keep them indefinitely. On a machine that has edited a few projects this is routinely tens of gigabytes, and every byte of it regenerates from the source media.

There is a setting for it: in the app's preferences, Media Cache, there is an option to delete cache files older than a chosen number of days. Setting that once is better than clearing it by hand every few months.

Scratch disks, and why the disk fills mid project

Photoshop writes working data to a scratch disk, which defaults to your startup drive. On a large document that can be many gigabytes while the app is open, and it is released when the app closes cleanly. A crash can leave the file behind.

If space vanishes while you work and returns when you quit, that is the scratch disk rather than a problem. Pointing it at an external drive in preferences is the standard fix on a Mac with a small internal drive.

Applications you no longer have

Adobe apps leave a lot behind when removed, and the Creative Cloud app's own uninstaller is more thorough than dragging an app to the Trash. Check for folders belonging to apps you have already removed:

ls ~/Library/Application\ Support/Adobe

Anything there for a version you no longer run is a leftover, which is the same pattern as any uninstall on a Mac. If video work is what fills the disk, render files and generated media covers the rest of that picture.