feat(mv3-part6): make injector controller explicitly async

[waabid]

Details

Makes inject async.

Motivation

Feature work.

Context

This method is async but not explicitly so. Changing it now such that we can make it clear moving forward which stores need to be async and which do not. Did some smoke testing in both mv3 and mv2 version of the extension; no errors were found.

Pull request checklist

• [ ] Addresses an existing issue: #0000
• [x] Ran yarn fastpass
• [x] Added/updated relevant unit test(s) (and ran yarn test)
• [x] Verified code coverage for the changes made. Check coverage report at: <rootDir>/test-results/unit/coverage
• [x] PR title AND final merge commit title both start with a semantic tag (fix:, chore:, feat(feature-name):, refactor:). See CONTRIBUTING.md.
• [ ] (UI changes only) Added screenshots/GIFs to description above
• [ ] (UI changes only) Verified usability with NVDA/JAWS