I don't know the specifics in Vancouver and times I stayed there are long enough ago that I've forgotten specific places.

However, more generally my experience has been almost every motel in US and Canada has allowed it. For example, in 2023 I took a six month trip through the US and was in a motel most nights. There was exactly one motel that didn't want my bike in the room. I turned it into problem-solving mode... namely since the bike was so important to my journey what alternatives could we devise? In this particular case, their alternative (storage shed but nobody to retrieve it until after 9am) was not acceptable and we then went to plan B where they gave me a recommendation of a different place to try.

In my other touring in US and Canada, I think I can count on two hands the times I couldn't bring bike in the room. In half those cases we were able to figure out an alternative. For example, there was a old lodge on the Alaska highway where the rooms were simply too small but it was OK to put it in the boiler room. Where you are traveling bike tourists are common so I'll be surprised if you encounter any situation on your trip where it isn't allowed.