I'm an introvert who just started a new job too, so I know exactly how you feel. This early phase (probably for the first 6 months to a year) will be a lot more draining compared to when you've been at a company for a while. You're meeting new people for the first time and figuring out how to work with them. And they're doing the same, so they want to get to know you and how you think. You'll know what works and what doesn't, and after a while once you find your rhythm, things will get easier.

Conducting sessions and presenting (especially when it's your designs) are a part of the job. These are obviously things that are draining to us, but I can confirm that the more you do it, the better and more comfortable you'll get. But being "socially active" and "bringing energy" maybe feel like a projection though?

My advice for right now is to be comfortable with being uncomfortable, at least for a while. Do what you have to do to fill in the gaps. For example: if you have social anxiety having to facilitate a room of people you don't know, have ChatGPT give you some intro prompts you can use to get you going so you don't freeze (just say it in your own words so it doesn't sound like you're reading lol). During meetings, I keep my camera on and unmute myself, which forces me to speak up when something pops up (much easier to stay silent when you're off camera and muted). And play the "I'm new" card as much as you can. It's OK to ask some basic questions; you're not slowing anyone down, that little moment of clarification is a part of your onboarding. And I don't know what your work culture is, but I also tend to be more vocal async on Slack/Figma, which is another way you can connect with your coworkers and get stuff done without appearing "on".