Subclass FunctionHandler to ensure it behaves like other handlers

[philippjfr]

We use custom bokeh handlers to allow us add our custom handling such as setting the curdoc, profiling, configuring session re-connects, track launching sessions etc. Until now function based apps bypassed all this meaning that they did not behave like other apps.

[codecov]

Codecov Report

❌ Patch coverage is 69.69697% with 10 lines in your changes missing coverage. Please review.
✅ Project coverage is 70.23%. Comparing base (77a8ff0) to head (61ee0bf).
⚠️ Report is 8 commits behind head on main.

Files with missing lines	Patch %	Lines
panel/io/handlers.py	65.51%	10 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #8249      +/-   ##
==========================================
+ Coverage   70.10%   70.23%   +0.12%     
==========================================
  Files         347      347              
  Lines       54092    54151      +59     
==========================================
+ Hits        37921    38032     +111     
+ Misses      16171    16119      -52     

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[philippjfr]

Test failures are unrelated. I'll open a new PR to fix that.