ci: add Lychee link checker for the docs #806

Job	Run time
PR title check	3s
Checks / Integration tests (3.11, ubuntu-latest)	2m 4s
Checks / E2E tests (3.11, ubuntu-latest)	4m 31s
Checks / Integration tests (3.14, ubuntu-latest)	3m 18s
Checks / Lint check / Lint check (3.14)	15s
Checks / E2E tests (3.14, ubuntu-latest)	5m 8s
Checks / Lint check / Lint check (3.11)	12s
Checks / Lint check / Lint check (3.13)	11s
Checks / Spell check	5s
Checks / Type check / Type check (3.13)	17s
Checks / Type check / Type check (3.11)	15s
Checks / Actions lint check	28s
Checks / Unit tests / Unit tests (windows-latest, 3.13)	1m 37s
Checks / Unit tests / Unit tests (windows-latest, 3.12)	1m 43s
Checks / Type check / Type check (3.12)	11s
Checks / Unit tests / Unit tests (ubuntu-latest, 3.13)	1m 17s
Checks / Doc check / Docs check	1m 0s
Checks / Unit tests / Unit tests (ubuntu-latest, 3.14)	1m 10s
Checks / Unit tests / Unit tests (windows-latest, 3.11)	1m 32s
Checks / Unit tests / Unit tests (windows-latest, 3.14)	1m 28s
Checks / Unit tests / Unit tests (ubuntu-latest, 3.12)	1m 15s
Checks / Type check / Type check (3.14)	13s
Checks / Unit tests / Unit tests (ubuntu-latest, 3.11)	1m 10s
Checks / Lint check / Lint check (3.12)	11s
Checks / Package check	23s
	29m 57s

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