Hey there!
So, if I have this right, it is only third party applications that Spotlight doesn’t find?
To confirm, these apps are stored on the internal startup disk, and not an external disk?
Do you have any such locations excluded System Preferences > Spotlight?
https://support.apple.com/en-me/guide/mac-help/mchlp2811/11.0/mac/11.0
If you go into System Preferences > Security and Privacy > General, are there any apps requesting approval there? (Allow this app):
https://support.apple.com/en-us/HT202491
Do you see these Applications in Finder? And are you able to open them and they function properly? (Just wondering if possibly they’re older 32 bit apps that can’t be found for whatever reason).
Likewise, I think it maybe informative if you see the actual location of these programs:
Open:
Apple Menu > About This Mac > System Report > Applications (Under the Software section).
Can you click on those Applications? Below you will see the file path to the App, (Macintosh HD > System > Applications, etc). Can you report the locations of those as opposed to the native Apple apps?
My first bet, as Spotlight appears to be working okay, just not on third party apps, is that either:
The apps aren’t compatible, hence unavailable.
The apps don’t have privileges/permissions.
They are installed on a location that Spotlight isn’t set, or allowed to search.
The formatting of a hard drive is in conflict with your Mac or vice versa.
Or finally Spotlight just isn’t working as it should.
If you’ve already (I assume) did a Spotlight Reindex of the startup disk:
https://support.apple.com/en-us/HT201716
And If those other answers don’t pan out, let me know, you maybe able to use the Terminal to sort it out, unless another solutionor path is presented, those answers may help us to with a resolution path. Cheers!