I was very interested to learn a while back at RoP that one of the reasons it was considered inappropriate for a man to appear in shirtsleeves before an unrelated woman was that in Regency times, men's shirts were so thin and see-through that they were basically considered undergarments.

I like note 80 on p.336, where a conduct book ordered gentlemen:

Never appear at breakfast, even in sultry weather, without your coat, waistcoat, collar and necktie. Are you a gentleman or a Hottentot? {my emphasis}

This makes it clearer why Darcy in P&P2 would be so embarrassed to appear coatless and vestless in front of Elizabeth after his dip in the pond, and adds another reason why he might feel at a disadvantage in the earlier scene where she walks in on him playing billiards at Netherfield, wearing a waistcoat but no coat - somebody obviously did their research! (I always enjoy that little scene - it shows so much in a few seconds!)