test: browser mode for dify ui

[hyoban]

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Summary

close #31926

Screenshots

Before	After
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Checklist

• This change requires a documentation update, included: Dify Document
• I understand that this PR may be closed in case there was no previous discussion or issues. (This doesn't apply to typos!)
• I've added a test for each change that was introduced, and I tried as much as possible to make a single atomic change.
• I've updated the documentation accordingly.
• I ran make lint && make type-check (backend) and cd web && pnpm exec vp staged (frontend) to appease the lint gods

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 85.43%. Comparing base (9612269) to head (159f33b).
⚠️ Report is 4 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #35365      +/-   ##
==========================================
- Coverage   85.47%   85.43%   -0.05%     
==========================================
  Files        4429     4430       +1     
  Lines      206405   206704     +299     
  Branches    38337    38470     +133     
==========================================
+ Hits       176429   176600     +171     
- Misses      26867    26995     +128     
  Partials     3109     3109              

Flag	Coverage Δ
dify-ui	92.55% <ø> (+0.04%)	⬆️
web	86.31% <ø> (-0.11%)	⬇️

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