refactor: make GitHub PR status more reliable and up to date (#613)

* fix: avoid incorrect PR status on default branch

Hide sidebar PR status when current branch is the repo default branch.
Tighten PR fallback matching to avoid picking unrelated PRs with the same branch name.

* fix: make sidebar PR status more reliable

Resolve PRs more reliably across remotes and repo networks.
Persist sidebar PR status across tab reloads while keeping updates fresh.
Reduce noisy GitHub errors and correct blocked styling in PR view.

* fix: correct blocked PR styling in sidebar

Stop treating missing merge permissions as a blocked PR state in the sidebar.
Align sidebar PR status colors and labels with the main PR view.

* refactor: make GitHub PR status updates feel more current

Refresh PR state on focus, visibility, and repo changes
Add follow-up PR refreshes after create, merge, ready, and update actions
Document GitHub PR resolution, consumers, polling, and triggers

packages/ui/src/lib/api/types.ts

@@ -774,6 +774,8 @@ export type GitHubPullRequestStatus = {
   pr?: GitHubPullRequest | null;
   checks?: GitHubChecksSummary | null;
   canMerge?: boolean;
+  defaultBranch?: string | null;
+  resolvedRemoteName?: string | null;
 };
 
 export type GitHubPullRequestCreateInput = {