Thank you for such a complete discussion. Also, thanks for saying don't attempt a reinstall, that would have been my first thought. Let's see...
I have a 2024 Mac, M4.
sw_vers reports 26.6.2 25G83
Startup disk reports "Macintosh HD MacOS 26.6.2" and nothing else.
list-full-installers was very interesting. It shows:
Title: macOS 27 Golden Gate, Version: 27.2, Size: 17389792KiB, Build: 26B123, Deferred: NO
* Title: macOS 27 Golden Gate, Version: 27.0.1, Size: 17955378KiB, Build: 26A434, Deferred: NO
* Title: macOS 27 Golden Gate, Version: 27.0, Size: 17969056KiB, Build: 26A428, Deferred: NO
* Title: macOS Tahoe, Version: 26.7.2, Size: 17958879KiB, Build: 25G332, Deferred: NO
* Title: macOS Tahoe, Version: 26.7.1, Size: 17950170KiB, Build: 25G241, Deferred: NO
* Title: macOS Tahoe, Version: 26.7, Size: 17951133KiB, Build: 25G229, Deferred: NO
* Title: macOS Tahoe, Version: 26.6.2, Size: 17953734KiB, Build: 25G83, Deferred: NO
* Title: macOS Tahoe, Version: 26.6.1, Size: 17938060KiB, Build: 25G76, Deferred: NO
* Title: macOS Tahoe, Version: 26.6, Size: 17942836KiB, Build: 25G72, Deferred: NO
and then a bunch of Sequoias that don't matter. Anyway, apparently there are several versions of Tahoe that never installed as well as none of the previous Golden Gates. Could something have happened at Tahoe 26.7 to block everything after that?
Privacy and Security: Photos exists and has permissions for Finder, which is all I am using. Mail does not exist in P&S. I have several Mail accounts. Initially, all were broken, but all but one are now working fine. Accessing the account via the provider's website shows that there are lots of messages, they just aren't downloading. Mail doesn't complain about not being able to access that account, it just never downloads any mail.
Photos is now weird. There should be one library, with several albums. However, Option + Photos brings up a box with three library entries. One brings up a "Welcome to Photos" screen, and seems to think I want to get started from new. The second brings up a dialog box that says "The library could not be opened". It doesn't do anything else, but at least appears to believe that a photo file does exist. The third opens...something. They are my photos, but the latest entry is for January, 2025. This is not correct. The library is, or should be, shared with my iPhone, which has many additional photos, including some from last Saturday.
So, Mail appears to be limited to one account, which I will investigate. Apparently none of the last half dozen versions of MacOS has installed, or has not installed properly. There is a photo library, someplace, but Photos doesn't appear to know that. I will try another user account, and add that result.