Switch to using the centralized tooling configs

[aryaemami59]

This PR:

• [X] Switches to using the centralized tooling configs.
• [X] Needs #4138.

Part 2 of 3

This PR follows #4138 and precedes #4607.

This is the second step in a three-part effort to centralize tooling configurations so they can be shared across multiple repos.

Previous PRs:

• Part 1: Creates dedicated repos housing shareable config files for ESLint, Prettier, TypeScript and Vitest.

Subsequent PRs:

• Part 3: Implements the necessary changes to comply with the new centralized configurations.