feat(repo): add quick repository switcher to repo header (#38188)

Add a GitHub-style quick repo switcher: a caret next to the owner/repo
breadcrumb
opens a dropdown that lists and searches the current owner's
repositories and
navigates to the selected one. The current repository is marked with a
check, and
private/fork repos show an icon.

Also, fix various bugs in fomtantic dropdown remote query

## Screenshots

<img width="505" height="198" alt="image"
src="https://github.com/user-attachments/assets/9f673d1b-fe60-41f0-b9e2-b00dc43720b5"
/>

Fixes #38187

---------

Co-authored-by: wxiaoguang <wxiaoguang@gmail.com>

options/locale/locale_en-US.json

@@ -1072,6 +1072,8 @@
   "repo.desc.internal": "Internal",
   "repo.desc.archived": "Archived",
   "repo.desc.sha256": "SHA256",
+  "repo.switch_repository": "Switch repository",
+  "repo.switch_repository.search": "Search repositories...",
   "repo.template.items": "Template Items",
   "repo.template.git_content": "Git Content (Default Branch)",
   "repo.template.git_hooks": "Git Hooks",