Thank you for the additional information.
Technically, in macOS 15 Sequoia, there was no App.app in the dock.
There was “Launchpad,” which, as we know, was removed in macOS 26 Tahoe .
The function of the now defunct Launchpad was integrated into Spotlight.
Perhaps this was an oversight on your part.
However, judging from all that is appearing in your question, it would seem that the issues of Spotlight that existed while in macOS 15 have somehow carried through into macOS 26.
Four things:
1. Under the current conditions and to test this, Finder >> Go > Applications. Are there duplication, triplicate lists of applications?
If not, it would seem reasonable to conclude that the Spotlight Index is indeed corrupted and needs to be rebuilt as suggested by Phil0124. 👍
2. After performing the above action and still no resolution regarding Apps.app in the dock producing the duplication, triplicate lists of applications.
3. Suggest you start over from scratch.
4 - As for the usage of PROSOFT recovery software If you have used or are using Time Machine Backup Utility you maybe able to Restore the Deleted Files
For future purposes
To truly protect your non replaceable Data
Have a 3-2-1 Rescue Plan in place and always current
3 Backups using 2 methods and 1 off site incase of natural disaster or un-natural disaster.
Each of the above should be done to a Dedicated Single Purposed External Drive
Below link is intended to augment what TM Backup does
https://bombich.com