refactor(api): refactor to avoid circular deps, add dpdm to lint step

[pichlermarc]

Which problem is this PR solving?

We had not run the dpdm-based cycle-check script for a while. This PR

• adds it to the lint step to ensure it runs in CI, prevent future regressions
• resolves existing circular deps in the API package (they were not an issue for end-users as they were types-only cicular deps)
• updates dpdm to the latest version

Supersedes #6363

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.68%. Comparing base (f9db1a2) to head (243cc05).
⚠️ Report is 7 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #6441   +/-   ##
=======================================
  Coverage   95.68%   95.68%           
=======================================
  Files         364      364           
  Lines       11775    11784    +9     
  Branches     2742     2745    +3     
=======================================
+ Hits        11267    11276    +9     
  Misses        508      508           

Files with missing lines	Coverage Δ
api/src/metrics/Metric.ts	100.00% <ø> (ø)

... and 1 file with indirect coverage changes

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[trentm]

One nit. THanks for re-instating that lint check.