[NO-TICKET] Upgrade React types to fix Storybook 8 branch

[pwolfert]

Summary

• Started out by upgrading the React types to the latest, trying to match @types/react and @types/react-dom as close as possible and made sure it was consistent everywhere
• Then I started trying to knock out the 109 TypeScript errors
• I found partway through that many of them could be reduced by cleaning up the yarn.lock file manually to get rid of old entries
• I went back and reverted a few of my changes, but many of them were actually necessary
• I changed the way the Dialog and Drawer stories are organized so that none of them pop up automatically. I then went back and added browser interaction tests to get the screenshots we want. Turns out that we were missing dialog screenshots for a while.

How to test

1. yarn type-check
2. yarn storybook
3. Anything else you can think to check

Checklist

Planning to merge it into the other branch, and I think we'll want to put that branch into v11

[pwolfert]

Status update:

6811f4b shows that there were some significant regressions in Storybook's ability to infer TypeScript types and document them. Instead of the type for Badge size being listed as big (only supports big), it is now reported as literal. For string | React.ReactNode, it only says union. Instead of type being checkbox and radio, it’s union. Instead of ReactNode for React.ReactNode, it prints out as ReactReactNode. Neither are the args tables showing inherited properties anymore from things like UseHintProps. That last one's a big deal. Overall, the prop tables in the Storybook docs are a much less accurate representation of our props, which makes this dead in the water for now.

I also did some investigating into the yarn lockfile changes, and I made sure that all the "docgen"-related packages were either going up in version number or staying the same, just to rule out the possibility that we might literally be going backwards.