crOS: Cleanup TokenHandleChecker tests

Cleanup TokenHandleChecker tests by extracting common variables.

Additionally -

1. Fix the response body of a test which produces HTTP_UNAUTHORIZED but
also a success response body.
2. Fix the structure of the tests a bit as per
go/unit-testing-practices?polyglot=cpp#structure
3. Rename `token_handle_checker_` local variable to
`token_handle_checker` to conform to the style guide.

Bug: 383733245
Test: unit_tests --gtest_filter="*TokenHandleCheckerTest*"
Change-Id: Ib97f5d6540a3b447371d9860409a27c1b49f9634
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6348736
Reviewed-by: Elie Maamari <emaamari@google.com>
Commit-Queue: Kush Sinha <sinhak@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1433406}