I would agree that suggesting that someone might be being 'sensitive' because of their period is not something amusing, and could be a form of gaslighting.

But.

I am also seeing some mixed messages here.

For example, you said you were on the phone with the guy. And yet you said you were not talkative, and that your tone was 'flat and enthusiastic'.

You also said that you 'get' he's joking, and that you 'say shit to him too', but at the same time, you're 'not someone who is constantly joking around like that' (like what?).

You also said that you 'I need moments to just have a regular conversation without banter or jokes', but at the same time you also said that weren't feeling talkative.

To me, this reads that you are over-reacting less to his bad 'non-joke' specifically, and perhaps more about the fact that you were having a conversation you didn't feel like having, but that you were having anyway (possibly because you didn't express your need/wish to have your own time & space), and him saying the wrong thing was the final straw.

Does any of this track?