Cannot confirm application installation with Apple Watch

While I was on the phone with Apple Support, the behavior I described in the original post disappeared, and my Apple Watch began to allow me to use it for authentication again. No changes were made to any of the participating hardware or firmware during the call. It just mysteriously began to work like it should. If there were a way to delete this thread, I would do so.

Some of your suggestions don't make sense, maybe because of menu differences in the newest versions of macOS and iOS.

Specific comments follow, numbered by your suggestions:

1) Resetting all devices makes no difference.

2) I can see that my watch is connected via Bluetooth to my iPhone, but there is no corresponding option in MacOS. Neither the iPhone nor the Watch are shown in the Bluetooth section of macOS Sytem Settings. But I presume this cannot be my problem because my watch does open my Mac when I get near it, and, as I said, my watch also responds for authentication when I log in to the forum here. There is no mention of Bluetooth at all on the watch or in the Wach app on the iPhone.

3) The "Allow Apple Watch to unlock your Mac" option is set and is working as it should, as I already mentioned. My watch reliably unlocks my Mac.

4) Since there is no entry for my Apple Watch (or my iPhone) in the Mac Bluetooth settings, there appears to be no way to follow your suggestion to reset the Bluetooth settings for the watch.

5) Wrist dectection is set. The watch has a passcode.

6) Software is up to date on all devices. (iOS 17.0.3, watchOS 10.0.1, macOS 14.0 Sonoma)

7) Reset Sync data is not an option. In Sonoma, the section is titled Privacy & Security, not Security & Privacy, so maybe there are some system menu rearrangements since you composed your advice. Under the current menu, there is no General section. There is and Advanced option, but it only has three options - Reqquire administrator password to access system-wide settings, Log out automatically after inactivity, and Log out after (setting for minutes). Nothing regarding Apple Watch.

8) I will contact Apple Support if I find that becomes necessary.

Until recently, my Watch correctly detected requests for authentication for software installations and updates. It recently stopped doing so. Thus my original post.

One more addition - I just tried to reset a System Setting, and the Watch did not respond, even though the dialog requisition authentication said it should. The image included shows this dialog, clearly showing that I should be able to use my Watch to authenticate.