Profile of Emissary

I'm pretty newb at this, so please be patient...

I was playing vs an expert British AI, and had the whole map dominated for several minutes during which I built up a bunch of panzer 4's. Then a churchill mk7 appeared and basically killed everything.

I played a 2nd game and tried only getting 2 p4's before teching up and using the rest of my pop on panthers, and what ended up happening was the churchills crushed the p4's, repaired up and then crushed the panthers.

I also tried getting AT guns but the churchills would just straight up kill the crews and run in guys to steal them to use against me. Similarly I thought StuG's were supposed to be anti tank, but they seemed to die instantly without doing any real damage.

I eventually managed to take a game by fully surrounding individual churchills with like a concave of panthers and panzergrenadiers since I had the economic lead in the early game, but that seems like a really roundabout way to counter a specific unit.

How do other people deal with them? Just based on reading tank comparisons it doesn't sound like people consider churchills particularly good, so I'm curious if I'm missing something super obvious.