More updates to unit tests for pending kernels work

[Zsailer]

This is a follow-up PR to #654. The session unit tests also need to changes for the work landing in Jupyter Client around pending kernels.

[Zsailer]

The await session_client.cleanup() is no longer needed because await jp_cleanup_subprocesses() handles cleanup.

[codecov-commenter]

Codecov Report

Merging #662 (e618ea5) into main (db46446) will decrease coverage by 0.08%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main     #662      +/-   ##
==========================================
- Coverage   77.88%   77.80%   -0.09%     
==========================================
  Files         110      110              
  Lines       10405    10415      +10     
  Branches     1400     1401       +1     
==========================================
- Hits         8104     8103       -1     
- Misses       1911     1924      +13     
+ Partials      390      388       -2     

Impacted Files	Coverage Δ
jupyter_server/tests/services/sessions/test_api.py	96.59% <100.00%> (-1.58%)	⬇️
jupyter_server/services/kernels/kernelmanager.py	80.63% <0.00%> (-1.91%)	⬇️
jupyter_server/tests/services/kernels/test_api.py	96.37% <0.00%> (+0.37%)	⬆️
jupyter_server/nbconvert/handlers.py	25.00% <0.00%> (+0.72%)	⬆️

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[blink1073]

Thanks!