You UserAgent used to post this thread appears to be Mozilla/5.0 (Windows NT 6.0; Win64; x64; rv:97.0) Gecko/20100101 Firefox/97.0

The NT 6.0 is Windows Vista

So either you modified you Firefox UA or the likely cause is you are running Firefox 97.0 in in Windows Vista compatibility mode for some reason. https://www.minitool.com/news/how-to-run-a-program-in-compatibility-mode.html

Once you fix this then you can download Firefox the current Firefox Release or the Firefox Extended Support Release from https://www.mozilla.org/firefox/all/

The installer (Firefox Setup 115.18.0.esr.exe) seems to think that my system is running Windows 7 and does not proceed.

The older Firefox 115.0 ESR is still be supported with security updates with the EOL Windows 7, 8, 8.1 (and macOS 10.12, 10.13, 10.14) OS users in mind as Windows 10, 11 users are being supported with the current Firefox 133.0.3 Release and 128.5.1esr https://support.mozilla.org/en-US/kb/firefox-users-windows-7-8-and-81-moving-extended-support

What is my "Firefox UserAgent" and why would it be modified to say I'm running Vista, which has never been installed on this system?

Should I just uninstall Firefox and start over?

This usually is a Compatibility Mode problem. Maybe at some point Windows suggested running Firefox in backwards compatibility mode to solve an issue? Bad idea. Let's fix that.

Right-click the desktop shortcut for Firefox and click Properties. If the shortcut is pinned to the taskbar, you have to right-click twice: once on the Firefox Taskbar button and once on Firefox on the context menu. It can be weirdly slow.

In the Properties dialog, change to the Compatibility tab.

If anything is selected in the Compatibility mode box, turn it off, you want it to run as a Windows 10 application.

If anything is checked under Settings, uncheck it.

Then click OK and do a normal exit/restart of Firefox.

Can you update now?

Note: Firefox 97 was on the standard release track, but the update server might send an intermediate version rather than jumping straight to the current version 133.

By the way, thank you for sharing your browser data. It indicates that one or more Enterprise Policies is active. Could you type or paste about:policies in the address bar and press Enter to load that page. The "Active" panel should list the policies overriding the default behavior of the browser. Anything relating to updates there?