You know what really helped for me?
Learning how to do ritual magic.
I should add, it's not real magic. I do LARP as a hobby, and my character is a ritualist. This means I, and a bunch of other people, put on little performances in a ritual circle to perform various magical effects in the game. (The way it works is that the referees score us on how good they thought the ritual was, and then tell us what happened.) A ritual is typically 10-15 minutes with about five people and, depending on what you're doing, can vary between completely scripted to totally improvised.
Pressure-wise, it's interesting. In the game, rituals are important and expensive. They matter, a lot. A screwed up ritual will backfire, including and up to getting you (or someone else) killed. At the very least a badly performed ritual won't work, but will still use up a lot of in-game money. Get it wrong, and there will be consequences.
Also, rituals don't always go according to plan. Summoning the spirit of someone from the dead? You let the referees know ahead of time and they'll make sure that the appropriate player is available to play the spirit. Once they go on stage, you need to improvise, and they might be rather angry at being summoned. So you never really know what's going to happen, and once you and your team get some practice, you get good at covering and supporting each other --- I once completely blanked on my lines and it was covered so smoothly that I don't think anyone noticed.
But at the same time, it's all completely pretend. It's not actually you in the ritual circle, it's your character. If things go completely pear shaped and you all get thunderbolted to death, you know you'll be drinking beer with the people involved later and the story of 'How I said the wrong thing and got fifteen people massacred' will have gone into legend.
So, at least for me, it provides an oddly safe environment to practice high-pressure performance and speaking. I know that in the couple of years since I've started doing this I've gotten way, way better and standing up in front of staring faces and doing my thing, and that skill does translate into real life.
Although I suspect that in real life there's less chance of demons suddenly materializing in the middle of the auditorium and trying to kill everyone (although I've been to meetings where that could have been a mercy).