fix(prompt-gate): pin duplicate prompt dispatches

Keep prompt reservations briefly after successful dispatch so rapid idle/message/error transitions cannot inject the same follow-up twice.

Route all production session prompt calls through the shared gate, restore skipped background resume state, release holds after abort/recovery paths, and preserve Ralph/ULW loop state when a dispatch is deferred.

Add regression coverage for session routing, static prompt route auditing, team-mode live messaging, model suggestion retries, call-omo-agent reuse, background parent wakes, runtime fallback, compaction recovery, Atlas, and Ralph/ULW loops.

test-setup.ts

@@ -6,6 +6,7 @@ import { _resetTaskToastManagerForTesting as resetTaskToastManager } from "./src
 import { _resetForTesting as resetModelFallbackState } from "./src/hooks/model-fallback/hook"
 import { _resetMemCacheForTesting as resetConnectedProvidersCache } from "./src/shared/connected-providers-cache"
 import { getOmoOpenCodeCacheDir } from "./src/shared/data-path"
+import { releaseAllPromptAsyncReservationsForTesting } from "./src/shared/prompt-async-gate"
 import { installModuleMockLifecycle } from "./src/testing/module-mock-lifecycle"
 
 const { restoreModuleMocks } = installModuleMockLifecycle(mock)
@@ -25,6 +26,7 @@ beforeEach(() => {
   resetTaskToastManager()
   resetModelFallbackState()
   resetConnectedProvidersCache()
+  releaseAllPromptAsyncReservationsForTesting()
 })
 
 afterEach(() => {
@@ -53,6 +55,7 @@ afterEach(() => {
   cleanupOmoCacheDir(getOmoOpenCodeCacheDir())
   resetTaskToastManager()
   resetConnectedProvidersCache()
+  releaseAllPromptAsyncReservationsForTesting()
   mock.restore()
   restoreModuleMocks()
 })