ci: add Lychee link checker for the docs #809

Job	Run time
PR title check	4s
Checks / Actions lint check	30s
Checks / Integration tests (3.14, ubuntu-latest)	3m 40s
Checks / Type check / Type check (3.12)	14s
Checks / Type check / Type check (3.11)	12s
Checks / E2E tests (3.14, ubuntu-latest)	5m 31s
Checks / Lint check / Lint check (3.14)	16s
Checks / Type check / Type check (3.13)	14s
Checks / Unit tests / Unit tests (ubuntu-latest, 3.12)	1m 11s
Checks / Integration tests (3.11, ubuntu-latest)	3m 41s
Checks / Lint check / Lint check (3.13)	16s
Checks / Unit tests / Unit tests (windows-latest, 3.11)	7m 51s
Checks / Type check / Type check (3.14)	12s
Checks / Lint check / Lint check (3.11)	10s
Checks / Unit tests / Unit tests (ubuntu-latest, 3.11)	1m 11s
Checks / E2E tests (3.11, ubuntu-latest)	4m 45s
Checks / Spell check	6s
Checks / Lint check / Lint check (3.12)	9s
Checks / Unit tests / Unit tests (windows-latest, 3.14)	1m 35s
Checks / Doc check / Docs check	58s
Checks / Unit tests / Unit tests (ubuntu-latest, 3.14)	1m 9s
Checks / Unit tests / Unit tests (ubuntu-latest, 3.13)	1m 13s
Checks / Unit tests / Unit tests (windows-latest, 3.13)	1m 48s
Checks / Package check	20s
Checks / Unit tests / Unit tests (windows-latest, 3.12)	1m 39s
	38m 55s

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