Prepare linter and TypeScript for docs. (#6804)
### Description
For ESLint, this is just a setup PR that caps the number of warnings
we're willing to accept.
For TypeScript, I unfortunately need to fix a whole mess of errors to
make ESLint run. Rather than fix all the errors, I'm just throwing down
a bunch of any's to keep the PR small.
CLOSES TURBO-1941
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Co-authored-by: Josh Goldberg ✨ <git@joshuakgoldberg.com>
