feat: Persisted devtools routing

[marc2332]

Closes #656

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 10 lines in your changes missing coverage. Please review.

Project coverage is 74.02%. Comparing base (9d37c3c) to head (632f5c1).
Report is 1 commits behind head on main.

Files	Patch %	Lines
crates/devtools/src/tabs/tree.rs	0.00%	7 Missing ⚠️
crates/devtools/src/lib.rs	0.00%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #657      +/-   ##
==========================================
+ Coverage   73.90%   74.02%   +0.11%     
==========================================
  Files         194      194              
  Lines       19951    19919      -32     
==========================================
  Hits        14745    14745              
+ Misses       5206     5174      -32     

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