fix: join the post room for what the Site Editor has open

[josephfusco]

Fixes #613

Switching entities inside the Site Editor leaves the previous room's row until it expires, so for up to the TTL someone shows in both places; templates still on the theme's file have no post ID and join no room until saved.

Use of AI Tools

AI assistance: Yes
Tool(s): Claude Code
Model(s): Claude Opus 5.5
Used for: Assisting with the Site Editor room and its tests.

[github-actions]

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.31%. Comparing base (c8ed2e5) to head (90ad55e).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff            @@
##               main     #638   +/-   ##
=========================================
  Coverage     95.31%   95.31%           
  Complexity      190      190           
=========================================
  Files            24       24           
  Lines          3265     3266    +1     
=========================================
+ Hits           3112     3113    +1     
  Misses          153      153           

Flag	Coverage Δ
multisite	95.31% <100.00%> (+<0.01%)	⬆️
phpunit	70.11% <100.00%> (+<0.01%)	⬆️

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[github-actions]

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