Adds read-only GET /user/orgs and GET /orgs/{org}/repos to
GiteaRepositoryBrowserApi (a third interface, OrganizationsRepository),
reusing existing repository mapping rather than duplicating it.
Repository list gains an organization filter chip row (all + one per
org), keeping the existing recent-push sort and paging. Organizations
are fetched once per session and cached; a failure to load them
degrades to an empty filter row instead of blocking the repository
list itself. Filtering only applies to the all-repositories mode,
since Gitea star is not organization-scoped.
Closes MVP outcome #2 in docs/product.md. No task file existed
beforehand; created it first per AGENTS.md.
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
