[3.x] Remove legacy code block badge style

[emmadesilva]

Summary

• Standardizes code-block titles on the responsive header introduced for v3.
• Removes the unnecessary label-style configuration and legacy badge rendering.
• Keeps custom presentations possible through the publishable code-block Blade view.
• Simplifies the code-block rendering API before v3 is released.

Validation

• Focused code-block, view-model, documentation, and includes tests pass (160 tests, 1,306 assertions).
• Framework suites: 3,806 passed; the known PHP 8.5 FeaturedImageUnitTest failure and a sandbox-restricted localhost socket test remain unrelated.
• php monorepo/HydeStan/run.php reports no errors.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 100.00%. Comparing base (9922cdf) to head (d9690af).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@             Coverage Diff             @@
##              master     #2584   +/-   ##
===========================================
  Coverage     100.00%   100.00%           
+ Complexity      1810      1807    -3     
===========================================
  Files            183       183           
  Lines           4483      4474    -9     
===========================================
- Hits            4483      4474    -9     

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