In your OP, you wrote that you were using version 2024.5.2 — that was the reason for my suggestion.
Opening it in a full browser tab gives you easier access to the Dev Tools, and I see in the remainder of your post(s) that you have already explored the information available there.
I’m curious — did you wait past the 20–30 sec delay time before closing the unlock screen and re-opening the extension?
It seems that these connection timeout errors are the source of the problem, and getting more information about these config calls under various conditions (gray screen, hung unlock screen, unresponsive icons, and when the extension is working normally, for comparison) is probably going to be the key to solving the issue, especially since it seems to have an intermittent character.
Maybe, maybe not. I’m not a dev (nor otherwise affiliated with Bitwarden), and I also have no personal experience with self-hosting. I have probably reached the limit of my ability to provide technical insight into this particular issue.
What I would recommend is that you examine those config calls (and anything else that seems suspicious) in your Network logs during various instances of the undesirable lags/freezes, and also look at the config calls in the Network logs when you are connected to the VPN, and on the other browsers with and without VPN.
Armed with these observations, you should reach out to Bitwarden’s customer support for further assistance. I would also highly recommend that your report this as a bug, by posting a New Issue on Bitwarden’s GitHub. In fact, I have a feeling that your issue is related to Issue #9561, so if you create your own issue report (including all of your Network log information from various tests), it may be a good idea to include a link to Issue #9561, as well; also link to this thread on the Community Forum.