The feedback about your personality is tricky, it could be seen two ways.
They can’t see your impact as easily. You’re doing the work, but it’s not being communicated well. You need to make your thinking visible for them to see your value.
You can try to emulate the extroverts on your own terms. Commit to raising your voice once a week. That could be sharing a new point of view on Slack, or asking a question in a design crit – taking a small step each week to demonstrate your insight and play an active part in the studio. It’s a shame that you need to do that, and I don’t want to tell you to be inauthentic. But if you want to progress in this specific environment, you might need to step out of your comfort zone. ‘The Charisma Myth’ by Olivia Fox Cabane is a great book that explores how to become ‘charismatic’ without changing your fundamental personality.
The second way the feedback could be interpreted is that you don’t match the “cultural fit” they have in mind. That’s a shortcoming on their side, but will be difficult to fight against. There are places out there that will value your skills more — that are more strategic, focussed on writing and research. If your current environment isn’t open to your way of working, then you might find a better fit elsewhere.
If you do decide to change roles, pay close attention to who interviews you. Are they built on a team of ‘superstar designers’ who care more about the case studies than the impact of work? Ask how they measure good creativity. If they have a “culture-fit”, ask them to describe it. You have an opportunity to take your learnings and find the right place for you, in a studio that wants you to work authentically.
You don’t have to be the loudest person in the room – but you do need to question if there’s space for different ways of working where you are. Or if you’re willing to bend to their monoculture.