build: Update TypeScript, use @typescript-eslint

[felixrieseberg]

Description of Change

This PR updates our TypeScript version to 3.3.3333 (don't ask), which is an all-around better version of TypeScript without breaking any code we have today.

That upgrade surfaced an issue with typescript-eslint-parser, which is deprecated and archived. The new kid on the block is typescript-eslint, which is better and actually found some issues in our code.

The only change that requires explanation is the removal of .eslintrc files that are overriding our module definition with script definitions. That declaration is incorrect as soon as TypeScript rolls around, which compiles in module mode (outputting a script, but that's none of ESLint's concern).

Checklist

• PR description included and stakeholders cc'd
• npm test passes
• PR title follows semantic commit guidelines
• PR release notes describe the change in a way relevant to app developers, and are capitalized, punctuated, and past tense.

Release Notes

Notes: no-notes

[felixrieseberg]

The mksnapshot test failure in arm is unrelated 🙇

[release-clerk]

No Release Notes