fix(website): use correct version for cross-package links

[Qjuh]

Please describe the changes this PR makes and why it should be merged:

Links to types in other subpackages use the correct version of that subpackage now, instead of the version of the current package.

Fixes for example https://discord.js.org/docs/packages/discord.js/14.14.1/Client:Class#rest

Also fixed two small issues for local testing of the docs website

Status and versioning classification:

• This PR only includes non-code changes, like changes to documentation, README, etc.

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Name	Status	Preview	Comments	Updated (UTC)
discord-js	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Mar 26, 2024 0:22am

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Name	Status	Preview	Comments	Updated (UTC)
discord-js-guide	⬜️ Ignored (Inspect)	Visit Preview		Mar 26, 2024 0:22am

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 7 lines in your changes are missing coverage. Please review.

Project coverage is 61.97%. Comparing base (a1a3a95) to head (6544c29).

Files	Patch %	Lines
apps/website/src/util/fetchNode.ts	0.00%	4 Missing ⚠️
apps/website/src/components/DocNode.tsx	0.00%	1 Missing ⚠️
apps/website/src/components/ExcerptNode.tsx	0.00%	1 Missing ⚠️
apps/website/src/util/fetchSitemap.ts	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #10193      +/-   ##
==========================================
- Coverage   62.35%   61.97%   -0.39%     
==========================================
  Files         209      210       +1     
  Lines       16280    16382     +102     
  Branches     1213     1214       +1     
==========================================
  Hits        10152    10152              
- Misses       6083     6185     +102     
  Partials       45       45              

Flag	Coverage Δ
website	0.00% <0.00%> (ø)

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