Migrate internal/flag to the new parse/format mechanisms

[FollowTheProcess]

• Add shared parse errors to flag
• Use parse and format in flag
• Tweak the type names definitions
• Migrate flag to the new parse/format mechanisms

Summary

[codecov]

Codecov Report

❌ Patch coverage is 97.64706% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 85.70%. Comparing base (72a4930) to head (cc50846).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
internal/format/format.go	87.50%	1 Missing and 1 partial ⚠️
internal/parse/parse.go	0.00%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #180      +/-   ##
==========================================
- Coverage   86.32%   85.70%   -0.63%     
==========================================
  Files           7        7              
  Lines        1514     1476      -38     
==========================================
- Hits         1307     1265      -42     
- Misses        145      148       +3     
- Partials       62       63       +1     

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