End user UI: Update logo loading spinner styling

[RachelElysia]

Issue

Closes #38693

Description

• No box
• Ensure it looks centered

Screenshot

Screen.Recording.2026-02-03.at.10.48.44.AM.mov

Testing

• QA'd all new/changed functionality manually

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 62.41%. Comparing base (1b27124) to head (db65f30).
⚠️ Report is 34 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #39234      +/-   ##
==========================================
- Coverage   62.41%   62.41%   -0.01%     
==========================================
  Files        2392     2392              
  Lines      186965   186965              
  Branches     8559     8457     -102     
==========================================
- Hits       116696   116691       -5     
- Misses      59106    59111       +5     
  Partials    11163    11163              

Flag	Coverage Δ
frontend	54.32% <100.00%> (-0.03%)	⬇️

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