You aren’t born a great speaker. It’s a learned skill that anyone can develop. Sure, extroverts have an upper hand at the start, but the perseverance of introverts allows them to catch up. The secret at becoming good at something outside your nature is twofold.
First off, you need to have the right motivation. If you want to become social in order to support your passion, it has less strain on you. You are even happy to act out of character because it gets you closer to your goal. This is where the danger of changing who you are to follow your passion comes in.
You have to recharge by coming back to your nature. This can come in many forms. You could close the door to your office in between meeting so you get some alone time. You could take walks or read a book during lunch instead of socializing. You may spend the weekend at home with a book instead of going out with friends.
No matter how you recharge, you need enough recovery to keep up your energy levels. Otherwise, your suppressed self will start coming out in other ways. It could even get to physical symptoms.
Become wise about how you balance your day, and there is nothing that you can’t achieve.