fix: propagate variant field in all promptAsync continuation paths (#3081)

All 5 continuation paths now send variant as top-level body field:
- boulder-continuation-injector.ts
- ralph-loop/continuation-prompt-injector.ts
- todo-continuation-enforcer/continuation-injection.ts
- unstable-agent-babysitter-hook.ts
- session-recovery/resume.ts

Plus type/helper updates in atlas, todo-continuation-enforcer,
unstable-agent-babysitter, and session-recovery.

TDD: 18 regression tests added, all pass. tsc clean.

src/hooks/unstable-agent-babysitter/index.test.ts

@@ -214,4 +214,45 @@ describe("unstable-agent-babysitter hook", () => {
     expect(promptCalls.length).toBe(1)
     Date.now = originalNow
   })
+
+  test("#given the main session model includes variant #when injecting a babysitter reminder #then promptAsync receives variant as a top-level field", async () => {
+    // given
+    setMainSession("main-1")
+    const promptCalls: Array<{ input: unknown }> = []
+    const mainModel = {
+      providerID: "openai",
+      modelID: "gpt-4",
+      variant: "max",
+    }
+    const ctx = createMockPluginInput({
+      messagesBySession: {
+        "main-1": [
+          { info: { agent: "sisyphus", model: mainModel } },
+        ],
+        "bg-1": [
+          { info: { role: "assistant" }, parts: [{ type: "thinking", thinking: "deep thought" }] },
+        ],
+      },
+      promptCalls,
+    })
+    const backgroundManager = createBackgroundManager([createTask()])
+    const hook = createUnstableAgentBabysitterHook(ctx, {
+      backgroundManager,
+      config: { timeout_ms: 120000 },
+    })
+
+    // when
+    await hook.event({ event: { type: "session.idle", properties: { sessionID: "main-1" } } })
+
+    // then
+    expect(promptCalls.length).toBe(1)
+    const payload = promptCalls[0].input as {
+      body?: {
+        model?: { providerID: string; modelID: string }
+        variant?: string
+      }
+    }
+    expect(payload.body?.model).toEqual({ providerID: "openai", modelID: "gpt-4" })
+    expect(payload.body?.variant).toBe("max")
+  })
 })