Can't find photos with keywords etc.. Is there a secure, non-malware, 3rd party photos app?

Could you update your Mac to Ventura? On macOS 13 Ventura you can search for photo keywords in all system apps, when you want to access the Photos Library. The new Photo Picker is one of the new features on macOS 13 Ventura. See: macOS Ventura - New Features - Apple

New Photos picker in system apps

A new Photos picker makes it easy to import photos and videos into system apps from your Photos library. Search your library to find just what you’re looking for

When I search for a keyword in Messages, I can even search for a part of the keyword.

You should be able to search for a keyword in the text box and get the photos with hat keyword:

Another method is to create a smart album with the following criteria: Keyword is XXXX

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

You won't get free, but an app like Mylio is consumer level, works on any device and very capable.