A MUI theme isn't by itself sufficient, since it really only modifies variables like shared design tokens would.
But it's rare that bespoke components would be 1:1 equivalent with the existing functionality/behaviors of a UI lib (unless that was a design constraint from the get-go, i.e. designers were only allowed to use existing functionality in that lib).
At our work, all components started out with MUI, but would often be extended with custom code based on the designers' needs. I could see no real way to sync that part of it with Figma (which would often just have basic wireframes and prototypes, maybe linked together in screens, hover states, etc., but not really implemented as interactive code).
It's kinda missing a storybook-like layer that can actually use and display different states, inputs, outputs, etc.
I actually advocated AGAINST a shared component system, predicting (accurately in hindsight) that the immature integration frameworks would not outlive the natural turnover of our teams and products, and would probably become tech debt before it even saw production use. Not a few months later, our entire department was dissolved, many product lines abandoned, etc. Luckily the teams that are still there were able to just keep going instead of wasting time on the doomed standardization effort...
But it couldn't do that. We talked to folks at Figma who were interested in the concept, but we never pursued it beyond early talks. I haven't kept up to see if they have gotten closer to that goal or not in recent years.