I'm a lead that's an introvert as well. I've figured out what really drains me are any meetings that I'm not in charge of (or haven't initiated the meeting). It probably has something to do with self-confidence and I will speak rarely or if I'm called upon.
Also for me it's hard to be energetic at the start of the day when meetings slowly appear on the daily agenda. The more I speak, the more confidence I get. But this is only in the case with a meet with many participants. I have no problems with 1:1 meetings.
Question for you - are meetings others initiate/are in charge of, but which nevertheless serve a clear point that necessitates your presence as draining?
Because that's the differentiator for me. If I have a goal I'm trying to achieve there, and the meeting is focused on that goal, it doesn't matter if I'm just a participant or not. If their isn't a clear goal, or I'm expected to be there despite not being involved in that goal (if it's an informational meeting I don't care about the information; if it's a decisional meeting I don't care or can't influence the decision; if it's a brainstorming meeting it's about something that doesn't affect me or a problem I'm not responsible to solve), it's massively draining.
Also for me it's hard to be energetic at the start of the day when meetings slowly appear on the daily agenda. The more I speak, the more confidence I get. But this is only in the case with a meet with many participants. I have no problems with 1:1 meetings.