Avoid calling the drain helper in WebSocketWriter if the protocol is not paused

[bdraco]

We already know its connected or it would have raised for is_closing so we can guard calling the coro with a check to see if its paused

[codspeed-hq]

CodSpeed Performance Report

Merging #9796 will improve performances by 22.38%

_{Comparing websocket_avoid_drain_helper (473191b) with master (d1eecea)}

Summary

⚡ 1 improvements
✅ 15 untouched benchmarks

Benchmarks breakdown

	Benchmark	master	websocket_avoid_drain_helper	Change
⚡	test_send_one_hundred_large_websocket_text_messages[pyloop]	658.5 µs	538.1 µs	+22.38%

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.69%. Comparing base (d1eecea) to head (473191b).
Report is 673 commits behind head on master.

✅ All tests successful. No failed tests found.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #9796   +/-   ##
=======================================
  Coverage   98.69%   98.69%           
=======================================
  Files         118      118           
  Lines       35997    35998    +1     
  Branches     4278     4279    +1     
=======================================
+ Hits        35526    35527    +1     
  Misses        316      316           
  Partials      155      155           

Flag	Coverage Δ
CI-GHA	98.58% <100.00%> (+<0.01%)	⬆️
OS-Linux	98.26% <100.00%> (+<0.01%)	⬆️
OS-Windows	96.04% <100.00%> (+<0.01%)	⬆️
OS-macOS	97.34% <100.00%> (+<0.01%)	⬆️
Py-3.10.11	97.18% <100.00%> (+<0.01%)	⬆️
Py-3.10.15	97.74% <100.00%> (+<0.01%)	⬆️
Py-3.11.10	97.79% <100.00%> (-0.01%)	⬇️
Py-3.11.9	97.23% <100.00%> (+<0.01%)	⬆️
Py-3.12.7	98.32% <100.00%> (-0.01%)	⬇️
Py-3.13.0	98.32% <100.00%> (+0.05%)	⬆️
Py-3.9.13	97.10% <100.00%> (+<0.01%)	⬆️
Py-3.9.20	97.66% <100.00%> (+<0.01%)	⬆️
Py-pypy7.3.16	97.27% <100.00%> (+<0.01%)	⬆️
VM-macos	97.34% <100.00%> (+<0.01%)	⬆️
VM-ubuntu	98.26% <100.00%> (+<0.01%)	⬆️
VM-windows	96.04% <100.00%> (+<0.01%)	⬆️

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[patchback]

Backport to 3.11: 💚 backport PR created

✅ Backport PR branch: patchback/backports/3.11/b947e476e7f891a80e894af02b6ae1e6ddce940e/pr-9796

Backported as #9797

🤖 @patchback
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