fix(asyncio): Remove shutdown handler

[sentrivana]

Remove the shutdown handler from the asyncio integration. Its only purpose was to log a message, but it looks like it has unintended side effects.

Closes #4234

[antonpirker]

Sad to see the message go, but if it removes side effects...

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 79.50%. Comparing base (0e7e2e6) to head (d5c0f53).
Report is 1 commits behind head on master.

✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4237      +/-   ##
==========================================
- Coverage   79.51%   79.50%   -0.01%     
==========================================
  Files         142      142              
  Lines       15884    15876       -8     
  Branches     2716     2716              
==========================================
- Hits        12630    12623       -7     
+ Misses       2391     2388       -3     
- Partials      863      865       +2     

Files with missing lines	Coverage Δ
sentry_sdk/integrations/asyncio.py	81.96% <ø> (+2.25%)	⬆️

... and 2 files with indirect coverage changes

[BYK]

I think add_signal_handler replaces any existing signal handlers (unlike the name suggests). There's a note on signal.signal() docs:

The previous signal handler will be returned (see the description of getsignal() above). (See the Unix man page signal(2) for further information.)

So maybe storing the previous signal handler and calling that (if it is not None) after logging the message could work?