Add algolia search to documentation

[adrianspdev]

Context

This PR includes new documentation search box with algolia

How has this been tested?

Locally

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature or improvement (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Additional language file or change to the existing one (translations)

Related issue(s):

1. https://github.com/handsontable/dev-handsontable/issues/1780

Affected project(s):

• handsontable
• @handsontable/angular
• @handsontable/react
• @handsontable/vue
• @handsontable/vue3

Checklist:

• Update the documentation to use Algolia for search.
• Search bar and results interface are visually integrated with the existing documentation website design.

[skip changelog]

[github-actions]

Launch the local version of documentation by running:

npm run docs:review 046fb5c89d74aa4a8a5052aa7c7ef12f51018160

[budnix]

@adrianspdev I deployed the changes to the staging, but it seems not working. There are plenty of errors coming into the console when I type something. Also, the styling appears to be broken. Could you check that?