Ultimately we'd like to keep it open and show an explicit working state as visualized in !587 (comment 2888415), but the latter is currently blocked by #41700.
I think that after my changes on the domain isolator we could already do something about that, even without reworking all the backend.
However, I'm going to see what I can do about #41700 today.
As I wrote in my long comment there, there are multiple layers of possible improvements, but it isn't a trivial issue.
Yeah in !587 (comment 2886963) I seemed to have gotten confused about what the behaviour in 12.0 was, it seems the site identity panel would stay open.
This makes it cumbersome to repeatedly request a new circuit to find unblocked exit nodes or faster circuits.
For anyone who wants an immediate work-around, you can use Ctrl+Shift+L whilst the circuit display is still open to request the new circuit.
For some reason I thought it closed itself too. Given that it stays open in 12.0, could we restore this behavior and Backport the fix to 12.5 stable please?
I'll open a separate ticket for the working state (for 13.0 or 13.5) if it still feels necessary.