Thanks Kevin. I should have been more precise.
Before I begin any experimentation, I already have two profiles: "Personal" and "Trusted". To trigger the delay, I exit Safari with a single window open set to "Trusted". When I start Safari as part of the test, it opens with a single window set to "Trusted". I do not manually open a window or switch profiles.
For the "Personal" profile test, which produces no delay, before the test I exit Safari with a single window open set to "Personal". When I start Safari as part of the test, it opens with a single window set to "Personal". I do not manually open a window or switch profiles.
When I wrote "Click on the extension button and use touch id to unlock", I was referring to the button in Safari's toolbar area.
The "Trusted" profile has 5 shared tab groups. When I am running the test, I do not switch to a shared tab. The window opens in a blank, unshared tab with no content displayed. That is the what is displayed when I click on the toolbar button.
I introduced this profile right after the feature was introduced in Safari. I've never run a beta version. The delay was noticed right from the start, right after I created that profile. It's persisted ever since.
I will do more experimentation this evening. I will create a brand new profile and see if the problem exists in that profile.
In case there's any ambiguity in my description, I'd be happy to provide a screen recording of the entire flow.