Fixes#869, #874.
Render EnterPlanMode as a compact desktop status instead of exposing model-facing plan-mode instructions, and refresh Windows frameless window drag hit testing after first show.
Tested: cd desktop && bun run test -- src/components/chat/PlanModePermissionDialog.test.tsx --run
Tested: cd desktop && bun run test -- electron/services/windows.test.ts --run
Tested: bun run check:desktop
Tested: bun run check:native
Confidence: high
Scope-risk: narrow