feat: add PR link checking workflow and fix links

[bjohansebas]

After asking for some feedback on the Astro Discord about a link checker, they recommended https://github.com/lycheeverse/lychee for this task. They also recommended https://github.com/HiDeoo/starlight-links-validator, but it seems it only works with Starlight.

closes #1100

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[socket-security]

Review the following changes in direct dependencies. Learn more about Socket for GitHub.

Diff	Package	Supply Chain Security	Vulnerability	Quality	Maintenance	License
	npm/​typescript-eslint@​8.53.1 ⏵ 8.57.0				+2
	npm/​@​iconify-json/​fluent@​1.2.38 ⏵ 1.2.40				+1
	npm/​@​types/​node@​25.3.2 ⏵ 25.4.0	+1		+1
	npm/​@​astrojs/​mdx@​4.3.13 ⏵ 4.3.14				+1
	npm/​eslint-plugin-astro@​1.5.0 ⏵ 1.6.0	-1			+5
	npm/​astro@​5.18.0 ⏵ 5.18.1				+1
	npm/​eslint@​9.39.2 ⏵ 9.39.4	+1
	npm/​postcss-custom-media@​12.0.0 ⏵ 12.0.1				+4
	npm/​@​eslint/​js@​9.39.2 ⏵ 9.39.4
	npm/​lint-staged@​16.2.7 ⏵ 16.3.3	+1			+8

View full report