include output json in caching hash

[atravitz]

this is a first pass at how we could implement what I described here: #1848 (comment)

Checklist

• All new code is appropriately documented (user-facing code must have complete docstrings).
• Added a news entry, or the changes are not user-facing.
• Ran pre-commit: you can run pre-commit locally or comment on this PR with pre-commit.ci autofix.

Manual Tests: these are slow so don't need to be run every commit, only before merging and when relevant changes are made (generally at reviewer-discretion).

• GPU integration tests
• example notebook testing
• packaging tests: run this for any large feature PRs or PRs that add test data.

Developers certificate of origin

• I certify that this contribution is covered by the MIT License here and the Developer Certificate of Origin at https://developercertificate.org/.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 91.91%. Comparing base (bd8efe6) to head (ef4f2cd).

Additional details and impacted files

@@                 Coverage Diff                 @@
##           quickrun_resume    #1890      +/-   ##
===================================================
+ Coverage            91.90%   91.91%   +0.01%     
===================================================
  Files                  206      206              
  Lines                18256    18287      +31     
===================================================
+ Hits                 16778    16809      +31     
  Misses                1478     1478              

Flag	Coverage Δ
fast-tests	91.91% <100.00%> (+0.01%)	⬆️

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[IAlibay]

To be discussed?