wrap lifespan decorator in docs and add missing type

[inktrap]

This is my solution for #1361 if you like it feel free to merge.

[inktrap]

I guess the test in docs_src/fastapi/docs001.py needs some changes too?

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 100.00%. Comparing base (9701e69) to head (3e6c61e).
Report is 16 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff            @@
##            master     #1362   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files          206       206           
  Lines        14940     14940           
=========================================
  Hits         14940     14940           

[codspeed-hq]

CodSpeed Performance Report

Merging #1362 will degrade performances by 23.88%

_{Comparing inktrap:master (3e6c61e) with master (81bb434)}

Summary

⚡ 1 improvements
❌ 1 regressions
✅ 82 untouched benchmarks

⚠️ Please fix the performance issues or acknowledge them on CodSpeed.

Benchmarks breakdown

	Benchmark	master	inktrap:master	Change
⚡	test_sum[500]	3.2 ms	2.7 ms	+17.3%
❌	test_first[1000]	3.1 ms	4.1 ms	-23.88%