Replace @gen.coroutine with async in Server.close

[hendrikmakait]

Drop the @gen.coroutine based Server.close method in favor of a native async version.

Refactoring extracted from ongoing work on #6359

• Tests added / passed
• Passes pre-commit run --all-files

[github-actions]

Unit Test Results

       6 files   -          9         6 suites   - 9   0s ⏱️ - 7h 5m 19s
   443 tests  -   2 358     395 ✔️  -   2 327    44 💤  -   34    4 ❌ +  3 
1 329 runs   - 19 441  1 181 ✔️  - 18 666  136 💤  - 786  12 ❌ +11 

For more details on these failures, see this check.

Results for commit 2564924. ± Comparison against base commit 36e9946.