fix: align sync fallback chain, fix model-fallback test determinism

- Hoist resolveFallbackChainForCallOmoAgent before sync/background branch
  so sync executor also receives the fallback chain
- Add fallbackChain parameter to sync-executor with setSessionFallbackChain
- Mock connected-providers-cache in event.model-fallback tests for
  deterministic behavior (no dependency on local cache files)
- Update test expectations to account for no-op fallback skip when
  normalized current model matches first fallback entry
- Add cache spy isolation for subagent-resolver fallback_models tests

src/tools/call-omo-agent/sync-executor.test.ts

@@ -9,6 +9,7 @@ describe("executeSync", () => {
       createOrGetSession: mock(async () => ({ sessionID: "ses-test-123", isNew: true })),
       waitForCompletion: mock(async () => {}),
       processMessages: mock(async () => "agent response"),
+      setSessionFallbackChain: mock(() => {}),
     }
 
     let promptArgs: any
@@ -53,6 +54,7 @@ describe("executeSync", () => {
       createOrGetSession: mock(async () => ({ sessionID: "ses-test-123", isNew: true })),
       waitForCompletion: mock(async () => {}),
       processMessages: mock(async () => "agent response"),
+      setSessionFallbackChain: mock(() => {}),
     }
 
     let promptArgs: any
@@ -88,4 +90,48 @@ describe("executeSync", () => {
     expect(promptAsync).toHaveBeenCalled()
     expect(promptArgs.body.tools.task).toBe(false)
   })
+
+  test("applies fallbackChain to sync sessions", async () => {
+    //#given
+    const { executeSync } = require("./sync-executor")
+
+    const setSessionFallbackChain = mock(() => {})
+    const deps = {
+      createOrGetSession: mock(async () => ({ sessionID: "ses-test-456", isNew: true })),
+      waitForCompletion: mock(async () => {}),
+      processMessages: mock(async () => "agent response"),
+      setSessionFallbackChain,
+    }
+
+    const args = {
+      subagent_type: "explore",
+      description: "test task",
+      prompt: "find something",
+    }
+
+    const toolContext = {
+      sessionID: "parent-session",
+      messageID: "msg-3",
+      agent: "sisyphus",
+      abort: new AbortController().signal,
+      metadata: mock(async () => {}),
+    }
+
+    const ctx = {
+      client: {
+        session: { promptAsync: mock(async () => ({ data: {} })) },
+      },
+    }
+
+    const fallbackChain = [
+      { providers: ["quotio"], model: "kimi-k2.5", variant: undefined },
+      { providers: ["openai"], model: "gpt-5.2", variant: "high" },
+    ]
+
+    //#when
+    await executeSync(args, toolContext, ctx as any, deps, fallbackChain)
+
+    //#then
+    expect(setSessionFallbackChain).toHaveBeenCalledWith("ses-test-456", fallbackChain)
+  })
 })