Do not flicker busy indicator during autoreload check

[philippjfr]

Fixes #3800

[codecov]

Codecov Report

Merging #3804 (2a07230) into master (5f330f2) will decrease coverage by 0.00%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master    #3804      +/-   ##
==========================================
- Coverage   82.97%   82.97%   -0.01%     
==========================================
  Files         221      221              
  Lines       32205    32208       +3     
==========================================
  Hits        26723    26723              
- Misses       5482     5485       +3     

Flag	Coverage Δ
ui-tests	34.16% <87.50%> (+<0.01%)	⬆️
unitexamples-tests	75.42% <100.00%> (-0.03%)	⬇️

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Impacted Files	Coverage Δ
panel/io/callbacks.py	78.94% <100.00%> (+0.48%)	⬆️
panel/io/reload.py	69.56% <100.00%> (-2.18%)	⬇️
panel/util.py	87.16% <0.00%> (-0.38%)	⬇️

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