chore(deps): Bump docsearch dependency to v4.7.0

[louismaximepiton]

Bump de docsearch deps and update all the needed things inside to look like the previous one.

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[Copilot]

Pull request overview

Updates the documentation site’s Algolia DocSearch integration to DocSearch v4.7.0, including dependency changes and refreshed SCSS overrides to match the new DocSearch styling/variables.

Changes:

• Bump @docsearch/js to ^4.7.0 and add @docsearch/css at ^4.7.0.
• Update DocSearch SCSS overrides and CSS custom properties for the v4 UI.
• Regenerate package-lock.json to reflect updated dependency graph.

Reviewed changes

Copilot reviewed 2 out of 3 changed files in this pull request and generated 3 comments.

File	Description
site/src/scss/_search.scss	Updates DocSearch CSS variables and component overrides for DocSearch v4 styling.
package.json	Bumps @docsearch/js to v4.7.0 and adds @docsearch/css.
package-lock.json	Lockfile updates for DocSearch v4 and related transitive dependency changes.

Suppressed comments (2)

site/src/scss/_search.scss:22

• Avoid hardcoding #000 in the backdrop color. Use an existing CSS custom property instead so theming/dark-mode can override it consistently.

  --docsearch-container-background: #{rgba(#000, .5)};

site/src/scss/_search.scss:159

• Avoid hardcoded 4px padding; use the existing spacing scale so this remains consistent if the base spacer changes.

  padding-inline: 4px;