I haven't lived in Montreal for many years, so [MENTION=10086]Admiral Ackbar[/MENTION] certainly has more experience there recently, but I did visit a couple of weeks ago and found central Montreal to be pretty normal.

Since you would also be visiting from out of province, I will make a recommendation on proof of vaccine: have something physical to show. Quebec's vaccine passport app is only available to Quebec residents. As a non-resident, you just have to show them satisfactory proof of your vaccination status (could be in an app, a CDC card, or some sort of electronic medical record, whether on your phone or printed - just not a QR code) but I suspect having a piece of paper is a lot easier.

I was there with a friend who got his shots in the US, and I had a much easier time getting into places by just showing a printout from my Alberta provincial health records than he did trying to show people whatever he has from the US on his phone. I was able to print it such that the text of what vaccines I got and when was large and easy to read, whereas he had to fiddle with his phone each time.