I had a 400W motor for a while, and that felt like a good solid continuous shove.
Given the other rider is also going up the same hill, they have to keep powering themselves too, so anything they give you is in addition to what they need to keep pace.
It doesn't take a lot though - a push can be enough to take the edge off your muscles for a moment.
So I'd guesstimate somewhere between 20 and 100 W, probably in the middle.
TBH I'd be more worried about random strange cyclists coming close enough to push me, and if I was offering the push that someone would take it the wrong way. I mean - where do you push? Their arse is probably convenient, but you're gonna get yelled at. Saddle would be a second best, or pushing their shoulder could put them off balance.
It would be different if you know the other rider.