fix: avoid auth errors for npm publish action

[bartveneman]

• node22 -> node24
• skip npm i -g npm because it fails
• remove registry-url because it causes auth errors
• move build step before versioning steps to avoid version bumps when build could potentially fail

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.70%. Comparing base (bb3d620) to head (51ead01).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #195   +/-   ##
=======================================
  Coverage   96.70%   96.70%           
=======================================
  Files           2        2           
  Lines         334      334           
  Branches      111      111           
=======================================
  Hits          323      323           
  Misses         10       10           
  Partials        1        1           

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[codecov]

Bundle Report

Bundle size has no change ✅