build(deps-dev): Update typescript and eslint dependencies

[brandonlenz]

Summary

Looks like there was some interdependency between #3452 and #3475, so I'm working them together in this PR

This should go out with a breaking release (at least I think so at the time of writing, we'll see what it takes to get things working)

Author & Maintainer checklist

• Is this is a breaking change?
  • Yes, and I accounted for the breaking changes according to the linked documentation
  • No
• Once merged, add the PR and Issue author(s) as a contributor(s) via the all-contributors bot

[brandonlenz]

Opened an issue because there appears to be a compatibility issue with the eslint-storybook-plugin and the latest version of eslint:

storybookjs/storybook#35097

[brandonlenz]

This should actually be completed after the npm upgrade, which sets some dependencies peer requirements right. #3500