Back in my younger days I knew a few drinkers who brought their own pewter mugs to the pub with them. Then there were other drinkers who kept their mugs at the pub.
The press accounts, including the court record, overwhelmingly all describe the mug as a "pot". Fewer accounts describe it as a "can".
Where the idea came from that it was a pail or bucket, is hard to guess.
So this "pot" may have been his, and may have (as you suggest) been quite empty.
All I can say to that is, you should try it sometime. See how far you get
You’re right. It was likely a pewter mug. But handy enough for all those semi-liquid bits&bobs.