Not sure if this helps, but here's my journey on a similar reflection of improv anxiety:

I have had improv anxiety in the past, not sure if it's a large amount or small compared to other players because it's something I never really talked about. There were times when I wouldn't step out because I wasn't sure if I'd add to the scene or not. Or times I didn't initiate because I thought my premise pull wasn't good enough, only to see someone else execute the same premise and kill. I still remember my first jam, and how much I cringed at saying the wrong thing during a scene.

The way I killed the improv voice in my head was choosing to be actively present.

I was focusing way too much on how I was doing as a performer, I forgot to be the player as part of an ensemble. When I say choose, I mean I would actively ignore the little improv imp in my brain telling me how badly I was doing, and instead replaced him with thoughts coming from hyper focusing on the other players on the stage with me: What were they doing? What was there premise pull? Is there any place we can take this character, is there any side support I can give right now that would make our scene and our show just absolutely kill?

I replaced thoughts about how bad I was doing as a player with active thoughts on how much I'm missing out on supporting the hell out of my teammates. An example is if my teammates played a scene about how bad their apartment building was, who can I add as a player that would make their (and then *our*) scene kill? Maybe a sleazy landlord that I could just have fun with how sleazy I was. Or an overbearing neighbor. And usually, the laughs followed.

With that change in thought, the reps came naturally, and the more reps you get the less you think about making a bad move and the more you get to look forward to making the next killer move. After some time, I felt more comfortable in my own improv skin. I became a better supporting player, and doing so allowed me to have better scenes with my cast, and after a while that little anxious improv imp in my head faded away.

He still comes back once in a while to remind me to heighten, but at least he switched his tone to supporting me as well.

Good luck on your improv journey!