refactor: switch to proper reconfig flow

[firstof9]

Breaking change

Use the new reconfigure flow as of HA 2024.4.x

Type of change

• Dependency upgrade
• Bugfix (non-breaking change which fixes an issue)
• New feature (which adds functionality)
• Breaking change (fix/feature causing existing functionality to break)
• Code quality improvements to existing code or addition of tests
• Documentation update
• Adds a new shipper
• Update existing shipper

Additional information

• This PR fixes or closes issue: fixes ISSUE: Configuring multiple carriers causes integration to not initialize  #934

[codecov-commenter]

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Codecov Report

Attention: Patch coverage is 38.23529% with 21 lines in your changes missing coverage. Please review.

Project coverage is 91.24%. Comparing base (8608d22) to head (d2d5be8).
Report is 14 commits behind head on dev.

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Additional details and impacted files

@@            Coverage Diff             @@
##              dev     #936      +/-   ##
==========================================
- Coverage   95.07%   91.24%   -3.84%     
==========================================
  Files           8        8              
  Lines        1482     1507      +25     
==========================================
- Hits         1409     1375      -34     
- Misses         73      132      +59     

Files	Coverage Δ
custom_components/mail_and_packages/__init__.py	91.48% <100.00%> (-0.62%)	⬇️
custom_components/mail_and_packages/config_flow.py	75.00% <25.00%> (-25.00%)	⬇️

... and 2 files with indirect coverage changes