Use recommended type-checked eslint

[tilacog]

Proposal for using the recommended-type-checked @typescript-eslint plugin, which is the suggested configuration for typescript projects.

Additionally:

• Type-check all test files.
• Adds the typescript-eslint-language-server as a development dependency for agnostic integration with editors and IDEs.

This PR will trigger many linter errors, and CI won't pass until we resolve them or adjust the error handling (either ignore or turn them into warnings).

Reference: https://typescript-eslint.io/linting/configs/#recommended-type-checked

[tilacog]

One possible approach would be to enable all lints as warnings (not errors) and gradually fix each category, then promote that category (now corrected) to errors.