Convert tests to Vitest

We have converted tests in the module template to Vitest. We should follow suit with this repo.

Note that this will require adding `allow-scripts` and upgrading our ESLint packages first.

- [ ] Ensure ESLint is configured for Vitest using `@metamask/eslint-config-vitest`
- [ ] Add `vite` and `vitest` as dev dependencies
- [ ] Convert existing tests to Vitest

Start by reviewing the module template's Vitest conversion and this repository's existing test setup. Then check the ESLint configuration and package dependencies against the issue checklist; done means the existing tests run under Vitest with the requested ESLint configuration and dependency changes.

Written by the indexing model from the issue text.