3rd party app access to Ventura Security & Privacy settings fails repeatedly

I’m having multiple Security & Privacy access failures running latest Ventura 13.5.1 on a 13” 2017 MBP and therefore cannot run certain 3rd party apps that require this access.

Any ideas on how to repair this and get my critical 3rd party apps back to life again?

WHAT HAPPENED 

Issue came to my attention when multiple 3rd party apps like Rectangle, Dropbox, Lunar, and others are partially or fully stuck because they can’t access various Security & Privacy system settings like Full Disk Access, and Accessibility.

Multiple methods of adding apps to the lists in those locations fail: I can’t drag an app icon onto the settings window nor add via “+” icon and Finder selection route. When I try, all works normally except no app appears afterward and the apps can’t function properly.

THINGS TRIED

• Restart Mac
• Disk Utility repair (mostly fine, see issue below*)
• Restart in Recovery Mode and run repairs (caveat same as above, see below)
• Run basic Maintenance Scripts and Disk Permissions routines
• Reset Accessibility via Terminal
• Remove TCC.db and other associated settings files via Terminal

*Disk Repair Issue:

My main drive “Macintosh HD” repairs run fine with no issues, however, “Macintosh HD - Data” does not in both normal operation and Recovery mode (see results below). 

Presumably this is not a problem because system files don’t reside there, but I wouldn't know. 

I’m confused by the error’s mention of TimeMachine snapshots on my main drive. I wouldn’t think there’d be any since I use an external drive for TimeMachine and have for many years. I don’t ever remember seeing TimeMachine snapshots in years of running repairs on main drive. Then again, maybe there’s some normal technical reason I wouldn’t know about.

Here’s the error Disk Util returns on "Macintosh HD - Data" partition:

Running First Aid on “Macintosh HD - Data” (disk1s5)

Verifying the startup volume will cause this computer to stop responding.

Verifying file system.
Volume could not be unmounted.
Using live mode.
Performing fsck_apfs -n -l -x /dev/rdisk1s5
Checking the container superblock.
Checking the checkpoint with transaction ID 26441588.
Checking the EFI jumpstart record.
Checking the space manager.
Checking the space manager free queue trees.
Checking the object map.
Checking the encryption key structures.
Checking volume /dev/rdisk1s5.
Checking the APFS volume superblock.
The volume Macintosh HD - Data was formatted by diskmanagementd (1677.50.1) and last modified by apfs_kext (2142.140.9).
Checking the object map.
Checking the snapshot metadata tree.
Checking the snapshot metadata.
Checking snapshot 1 of 13 (com.apple.TimeMachine.2023-08-24-085318.local)
Checking snapshot 2 of 13 (com.apple.TimeMachine.2023-08-24-095538.local)
Checking snapshot 3 of 13 (com.apple.TimeMachine.2023-08-24-110552.local)
Checking snapshot 4 of 13 (com.apple.TimeMachine.2023-08-24-120558.local)
Checking snapshot 5 of 13 (com.apple.TimeMachine.2023-08-24-131150.local)
Checking snapshot 6 of 13 (com.apple.TimeMachine.2023-08-24-141735.local)
Checking snapshot 7 of 13 (com.apple.TimeMachine.2023-08-24-151802.local)
Checking snapshot 8 of 13 (com.apple.TimeMachine.2023-08-24-170410.local)
warning: mismatch between extentref entry reference count (0) and calculated fsroot entry reference count (-1) for extent (108128211 + 3)
warning: mismatch between extentref entry reference count (0) and calculated fsroot entry reference count (-1) for extent (110185925 + 1)
Checking snapshot 9 of 13 (com.apple.TimeMachine.2023-08-24-182632.local)
error: mismatch between extentref entry reference count (0) and calculated fsroot entry reference count (1) for extent (108128211 + 3)
error: mismatch between extentref entry reference count (0) and calculated fsroot entry reference count (1) for extent (110185925 + 1)
Checking snapshot 10 of 13 (com.apple.TimeMachine.2023-08-24-193121.local)
Checking snapshot 11 of 13 (com.apple.TimeMachine.2023-08-24-203222.local)
Checking snapshot 12 of 13 (com.apple.TimeMachine.2023-08-24-214518.local)
Checking snapshot 13 of 13 (com.apple.TimeMachine.2023-08-25-085056.local)
Checking the document ID tree.
Checking the fsroot tree.
Checking the extent ref tree.
Verifying volume object map space.
The volume /dev/rdisk1s5 was found to be corrupt and needs to be repaired.
Verifying allocated space.
Performing deferred repairs.
error: Unable to perform deferred repairs without full space verification
error: Try running fsck against the entire APFS container instead of a volume
The volume /dev/rdisk1s5 could not be verified completely.
File system check exit code is 8.
Restoring the original state found as mounted.
File system verify or repair failed. : (-69845)

Operation successful.