refactor: remove comment and promises, instead only using async/await

[shogo-nakano-desu]

Description

• There is a comment by @bcoe that says TODO here. So I deleted Promises and changed to use async/await only.

Check list

• [x] Make sure to open an issue as a bug/issue before writing your code! That way we can discuss the change, evaluate designs, and agree on the general idea
  • Here is the issue https://github.com/googleapis/google-auth-library-nodejs/issues/1434
• [x] Ensure the tests and linter pass
• [x] Code coverage does not decrease (if any source code was changed)
  • To be precise, code coverage "rate" in googleauth.ts decreases even though uncovered lines stay the same because lines of code decrease. But I think it is not a problem because actual coverage does not become worse.
• [x] Appropriate docs were updated (if necessary)
  • Do not need to update in this PR

Refactor #1434 🦕