perf(code): make task composer repo/branch selectors feel instant

[fercgomes]

Summary

• Fetch cloud branches as soon as a repo is selected — first page contains default_branch, so the branch button shows main/master immediately and the dropdown opens against a warm cache.
• Add staleTime: 5 min to useGithubBranches and useUserGithubBranches so reopens within 5 min skip the network.
• Drop the open gate on the local-mode branches query in BranchSelector (it's a fast local git call) and bump staleTime to 60s.
• Remove the now-dead isCloudBranchPickerOpen state in TaskInput.

Why

The branch dropdown was empty until the user clicked it, and the trigger button stayed blank until that round-trip returned. Reopening refetched from scratch because the infinite query had no staleTime.

Test plan

• pnpm --filter code typecheck passes
• In cloud mode with a remembered repo, the branch button shows the default branch within one round-trip without clicking the dropdown
• Opening the branch dropdown a second time within 5 min shows results without a loading row (warm cache)
• Switching repos fires one branches request and updates the button when the new repo's first page returns
• In local/worktree mode, the branch button populates without opening the dropdown

[greptile-apps]

_{Reviews (1): Last reviewed commit: "perf(code): make task composer repo/bran..." | Re-trigger Greptile}