build: upgrade to TypeScript 5.3

[erickzhao]

This PR migrates to TypeScript 5, which is a prerequisite for upgrading to Docusaurus 3.

• This adds a major version bump to @tsconfig/docusaurus, which now uses the bundler module resolution strategy from TS 5.
• @typescript-eslint was upgraded to support TS 5.
  • This is the smallest major version bump that would allow this to work.
  • Note that because this version of @typescript-eslint does not support TS 5.4, we're a bit behind in TS versions.
• Removes Jest dependencies since we weren't using them. Can be added back at any point if we add unit tests to the code.

Future work:

• Upgrade ESLint and @typescript-eslint
• Upgrade to TS 5.4.5