docs: Added package manager tab group synchronization across the entire installation page

[BlazerYoo]

Overview

Updates the docs installation page so choosing a package manager in one code group automatically updates the other code groups on the same page.

Manual Testing

1. Run the docs locally with bun run docs:dev
2. Open the installation page at /guide/installation
3. Click Bun in one code group under “From Scratch”
4. Verify the other code groups on the page switch to Bun as well
5. Repeat with PNPM or NPM to confirm the selection syncs across all groups
6. Refresh the page and repeat to make sure it still works after reload

Related Issue

This PR does not close a tracked issue.

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commit: 86f203c

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 78.46%. Comparing base (c8e93b1) to head (86f203c).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2421      +/-   ##
==========================================
+ Coverage   78.33%   78.46%   +0.12%     
==========================================
  Files         133      133              
  Lines        3882     3882              
  Branches      875      875              
==========================================
+ Hits         3041     3046       +5     
+ Misses        752      749       -3     
+ Partials       89       87       -2     

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[PatrykKuniczak]

Move everything to /utils and there simply call that function in enhanceApp section.
Also if(typeof window ... move inside that helper, to keep index.ts clean 😄

And run prettier.

Anyway that's amazing feature(not a fix, like you've suggested i need to change the PR title), i've seen that in many docs of multiple tools,

[BlazerYoo]

Thanks for the review! Just pushed a commit covering all of it:

• Moved all sync logic into docs/.vitepress/utils/code-groups.ts, exposing a single setupCodeGroupSync() that enhanceApp calls
• Moved if(typeof window ... inside the helper, index.ts clean
• Ran prettier; --check passes

[PatrykKuniczak]

LGTM 😃

[PatrykKuniczak]

@BlazerYoo That's not your problem with CI.
I'll take a look on that, maybe tomorrow