[Theory crafting]Connecting Pokémon GO and Pokémon Sleep

So I've been using Pokémon Sleep for the last two weeks, and I'm generally enjoying it, but I've been thinking it might be fun if Pokémon Sleep and Pokémon GO connected a bit more. I know they are developed by two different dev teams, but when I found out that the Pokémon GO Plus + worked with both games, it made me curious about ways the games could work together.

The easiest thing I can think of would just be some kind of streak bonus shared between each game. Like if you get a good night's sleep, then you get an extra catch bonus on your first catch of the day, and when you walk enough during the day, you get an extra set of berries to feed your Snorlax.

Does anyone else feel like this could be a fun idea, or do you have any other ideas of ways they could connect?