Fix outdated publish action

[asabaylus]

• Update Node.js from 18.x to 20.x to match package.json requirement (>=20)
• Remove redundant cache action (setup-node has built-in caching)
• Add required permissions for GITHUB_TOKEN (contents, packages, pull-requests, issues)
• Add registry-url and NODE_AUTH_TOKEN for proper npm authentication
• Split release steps for better clarity and debugging

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 100.00%. Comparing base (22f943e) to head (4c42223).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff            @@
##              main     #1611   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files            7         7           
  Lines          238       238           
  Branches        47        47           
=========================================
  Hits           238       238           

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