My Apple Watch fits into my multi plug wall plug, but my watch won’t charge?

Your best bet is to use the small wall charger that came with your iPhone with the watch's charging puck in a standard electrical wall outlet. The watch's software can be very picky about what is used to charge the watch.

M1 Mac mini, macOS 14.5;  Watch, series 7 GPS/cellular, watchOS 10.5; iPhone 12 Pro, iOS 17.5; TV 4th Gen, tvOS 17.5; HomePods, audioOS 17.5 and Airport Express w/ Airplay 2

You need to use the charging puck that came with the watch to charge an Apple Watch. If that is what you are plugging into the multi-plug charger then the charger may not have adequate power to charge the watch. In that case you need to. carefully check the chargers specifications.