web: Router prep for Command Palette

[GirlBossRush]

Details

This PR prepares the router for use in the upcoming command palette (#20685).

The changes here are largely mechanical and align with the recent improvements to the flow executor.

Changes

• A default export is added to every route handler
• Lit's development warnings regarding @property setters defined without getters have been corrected.
• Route definitions now have less repetition and use a nested structure to build out path patterns

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 93.11%. Comparing base (ce1237e) to head (1d84cc4).
✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #20723      +/-   ##
==========================================
- Coverage   93.39%   93.11%   -0.28%     
==========================================
  Files         983      983              
  Lines       55477    55477              
==========================================
- Hits        51813    51658     -155     
- Misses       3664     3819     +155     

Flag	Coverage Δ
conformance	37.38% <ø> (-0.31%)	⬇️
e2e	42.67% <ø> (-0.60%)	⬇️
integration	22.39% <ø> (-0.05%)	⬇️
unit	91.54% <ø> (+<0.01%)	⬆️
unit-migrate	91.63% <ø> (+<0.01%)	⬆️

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