feat(prover): remove more database related code

[davidtaikocha]

No description provided.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 50.17%. Comparing base (2d00517) to head (d3d2e31).

❗ Current head d3d2e31 differs from pull request most recent head feefcbd. Consider uploading reports for the commit feefcbd to get more accurate results

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #623      +/-   ##
==========================================
+ Coverage   50.14%   50.17%   +0.02%     
==========================================
  Files          55       55              
  Lines        5763     5756       -7     
==========================================
- Hits         2890     2888       -2     
+ Misses       2564     2560       -4     
+ Partials      309      308       -1     

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