Puppy and cat socializing

I have a 4 month old chiuaua/pug mix who loves playing my 5 year old tuexedo cat. The problem is my cat will often go into the living room, then my puppy with chase him into our bed room (that used to have a baby gate). Whenever my cat gets into the bedroom I shut the door to keep my dog from chasing him in there. my cat then starts to meow so sadly at the door like he wants to come out and the cycle repeats. my cat also likes to play with my puppy and will paw under the door to play that way or if my puppy is in his crate he will paw the crate. if my puppy isn’t looking his direction my cat will start meowing and Trilling then run away. I thought this was all playing but last week they were ”play“ wrestling and my cat started to growl at my puppy. he has NEVER done that before. I’m looking for some clarity on if my cat is playing or really dislikes the dog? we had to take down the baby gate because my dog leanred he can jump over it. my cat has multiple places to get on higher ground but he never does, he always chooses to run into the bedroom.