You can not exit the restricted area yourself, an airline company staff is needed to escort you back to arrival area.

Lounge staff might not be familiar with the procedure, (as the staff who normally deal with this situation is someone who deals with flight cancellation, flight delay) before they figure out what do to, you have no choice but to stay in the lounge, once they figure out what to do, you would need to wait until a staff is available to escort you.(my experience from CX at HKG is your escort would never be a lounge staff, it would be someone who normally escort you when you have a tight connection)

Worst case, your request to leave departure is denied...

I would not be surprised that it is already 11am (after your shower and croissant) when you about to go through immigration for the second time, you could easily spend 20 minutes waiting to go through immigration.

If you think that croissant is worth the wait and risk, then go for it, please do report back to let us know how the experience was.