Thank you for the continued responses. I performed some very basic testing using a Debian 12.8.0 Live CD. The results were confusing and highlighted some issues with the creation of network profiles in general, at least from my point of view.
The short version is that if the behavior with "Connect Automatically" and "Make available to other users" is down to NetworkManager, then I sympathize with the suggestions to migrate from it to systemd-networkd. If someone could point me to a simple guide for that I'll look into it. Regarding reporting a bug, I have to say I'm not inclined to this, because I've learned from others this can get quite involved and lead to demands on the submitter's time. On the other hand, I think the behaviors I've experienced ought to be addressed at some point, because the confusion is bound to affect other users, especially those trying Debian for the first time. The long version, which is a description of the testing, and the results of my testing on the Live CD: All testing was performed using the Network panel in the Settings application. The default Debian Live user has admin privileges, so I used this for my initial testing. I configured the default wired network profile with a manual IPv4 address and _disabled_ "Make available to other users". As expected, the wired connection was automatically activated once the physical connection was made to the server. Within the same boot session, I created and switched to a new user via the GUI, a standard user with no admin privileges. The same default wired network profile was re-configured with "Make available to other users" _enabled_. As expected, the wired connection from within this standard user account was automatically activated once the physical connection was made to the server. So far, everything has worked as expected. But then I tested the scenario I was having trouble with. As the same standard user, I set the default wired network profile so that "Make available to other users" was now _disabled_. Contrary to my expectations, the wired connection was still automatically activated once the physical connection was made to the server. This seems to be at odds with the idea expressed by Lee and possibly Michael Stone that, when the the current GUI user doesn't have the correct privileges, "Connect Automatically" would fail in this case, but it's possible I've missed something. When I attempted to make changes to the Details tab as the standard user I came across something I think is surely a bug, though. The Details tab of a network profile created by a standard user is available to view by the standard user, but attempting to modify the available settings triggers a prompt for admin authentication, and here's the problem: if the standard user chooses to Cancel the prompt (I tap the Escape key), then _the GUI shows the setting as modified when it is not_. I was able to determine that this is a visual feedback error because testing showed that the behavior of the network profile respected the settings in place _before_ the unauthenticated changes. This lack of accurate visual feedback survives the closing and re-opening of the network profile being modified. I tested this with the "Connect Automatically" and "Make available to other users" settings. Other issues I experienced during this testing were: Admin credentials appear to be silently cached, similar to sudo, when authenticating in the Settings application. This is confusing and can make it difficult to perform troubleshooting. I would personally prefer credential caching in the GUI to be turned off, or visible to the user with the option to clear the cache. Although I hate this behavior in Windows, not caching the credentials is definitely preferable, in my opinion, to silently caching. I think on Macs, users enable and disable admin privileges to modify system settings with a GUI padlock (but this was years ago, it might have changed), and I always thought that was an elegant solution. During the creation of the test network profile as a standard user, I was not allowed (in fact I wasn't even offered the option) to configure the settings on the Details tab - this is where the "Connect automatically" and "Make available to other users" settings are. These settings appear to be available only to admin users. I found this confusing - does the standard user have ownership of a network profile they create or not? Why would these options only be available to admin users? The active connection GUI in the Settings application's Network tab changes from a sliding button to a check mark when more than one network profile is configured. In fact, the sliding button disappears altogether. Also, the visual feedback of "Cable unplugged" and "100 Mbps"/"1000 Mbps" indicating a cable's physical connection status disappears. Without trying to be offensive, I actually encountered so much strange behavior during my testing that I would gladly migrate to something less confusing to use. If there's an easy way to submit these issues without tying myself to a prolonged need to submit feedback and do independent testing, please let me know. I'd also be grateful to be told where exactly to file that feedback.
