linkcheck: update implementation to make use of py311 features #11903

Job	Run time
Coverage	0s
Python 3.14 (Docutils 0.20)	2m 30s
Python 3.14 (Docutils 0.20; free-threaded)	3m 35s
Python 3.14 (Docutils 0.21)	3m 2s
Docutils HEAD	3m 29s
LaTeX	4m 40s
Python 3.14 (Docutils 0.21; free-threaded)	3m 38s
Oldest supported	3m 17s
Python 3.11 (Docutils 0.20)	2m 33s
Windows	6m 20s
Python 3.11 (Docutils 0.21)	2m 51s
Python 3.12 (Docutils 0.20)	3m 3s
Python 3.12 (Docutils 0.21)	3m 27s
Python 3.13 (Docutils 0.20)	2m 53s
Python 3.13 (Docutils 0.21)	3m 19s
	48m 37s

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