Allow (auto) saving and loading a RunManager (e.g., for external monitoring)

[basnijholt]

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 81.25000% with 6 lines in your changes are missing coverage. Please review.

Project coverage is 72.78%. Comparing base (97b20d8) to head (f01843d). Report is 2 commits behind head on main.

:exclamation: Current head f01843d differs from pull request most recent head 978cc37. Consider uploading reports for the commit 978cc37 to get more accurate results

Files	Patch %	Lines
adaptive_scheduler/_server_support/run_manager.py	80.64%	6 Missing :warning:

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #156      +/-   ##
==========================================
- Coverage   74.72%   72.78%   -1.94%     
==========================================
  Files          22       22              
  Lines        2777     2506     -271     
==========================================
- Hits         2075     1824     -251     
+ Misses        702      682      -20     

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