🚀 Feature: Add a Cmd/Ctrl + K search shortcut to the site

[JoshuaKGoldberg]

Bug Report Checklist

• I have tried restarting my IDE and the issue persists.
• I have pulled the latest main branch of the repository.
• I have searched for related issues and found none that matched my issue.

Overview

Following up on #70 (comment):

Adding a Ctrl/Cmd+K shortcut for search the way Docusaurus and a lot of other sites / site generators have

Is there an existing Typedoc plugin for this? I'd much rather reuse an existing one than than make one anew.

Additional Info

No response