This is the first time I’ve ever thought that anyone would find it acceptable to bring a bicycle into a shop. I don’t find it acceptable.
Depends on the shop. On my old commute I sometimes stopped off at the local corner shop so no chance of ever getting a bike in there.
But I also sometimes stopped at an Asda on the way and routinely wheeled the bike in, parked it near the entrance, bought my meal deal and went on my way. Never once had any issues (although it was early in the morning, maybe they’d have said something if I’d have tried it on a busy Saturday…)
I’d never expect to wheel a bike around the shop with me but – assuming of course that the shop is a reasonable size, and is not a stockist of expensive artwork / fine bone china / etc – wheeling it “just inside” and asking if it’s OK to just pop it there for a minute is seldom met with any complaint.
I used to do some food bank collection/delivery work on a community e-cargo bike, took that into the supermarket every time!