“Adobe Application Support” is not optimised for your Mac

Not sure if this is of any use, the Adobe forum appears to be discussing same.

https://forums.adobe.com/thread/2540909

From the above link this post seems to offer a “fix” and/or a location for the offender.

When you try searching in Finder for the “Adobe Application Manager Utilities” app have you enabled “system files” so they are included in the searched locations, you could also try via Spotlight.

Saying that after reading up further I don’t believe you can just delete that one aspect of Creative Cloud or the installed software, Adobe warn about that (see below).

They do provide a Creative Cloud Cleaner Tool which gives you the option to remove individual packages though.

https://helpx.adobe.com/creative-cloud/kb/cc-cleaner-tool-installation-problems.html

This talks about troubleshooting Adobe Application Manager download and installation issues but also warns that it’s required for the Creative Cloud to function.

https://helpx.adobe.com/uk/creative-suite/kb/aam-troubleshoot-download-install.html

This is the relevant section.

So, if you want the warnings to stop now it looks as though you have to remove everything, if you can’t do that because you need the software it’s a wait on Adobe until they update that part to 64bit.

Sorry, but can’t see what else you can do.

I suggest using EtreCheck to produce a report. You can then review the report to help locate these "hidden" files.

Ref: Using EtreCheck to Troubleshoot Potential… - Apple Community