Me(20M) and my boyfriend(27M) can’t make each other laugh

It all started in december when we started to talk on Tinder(while he was in an abusive and toxic relationship). I made him quit that and he’s really grateful for that, so there’s nothing bad in what I did. He had been doing it for 1,5 year until then and I had to force him to make a decision between me and his ex.

He chose me, but since then we haven’t even made each other laugh, he’s really introvert and I’m really-really not. Sometimes it feels like I have to be an introvert to get close to him and it makes me really anxious. We match, we play with the same games, listen to the same music. But even in games he plays alone and don’t even let me play with him, he does everything on his own. It’s really hard to think of losing him, although my mental health is the most important for me.

He takes care of me, as it seems to be he loves me, but my mental health is unstable due to these things. I’m an extrovert and I have to start every single conversation and as he states :”I ain’t got no problem with you, it’s all perfect”.
I always try to communicate, but “I’ll try harder and everything will be alright” won’t solve these things all the time.

I don’t know what to do and how to do it.
Tldr: I’m the biggest fan of cats, but he’s allergic to them. If I had known that he is, I’d never date him..

Any ideas?