feat: add pluggable multi-CLI backend system

Implement BackendAdapter interface with four CLI backends:
- ClaudeCodeBackend (extracted from AgentRuntime)
- CodexBackend (OpenAI Codex CLI)
- GeminiBackend (Google Gemini CLI)
- OpenCodeBackend (OpenCode CLI)

Add BackendRegistry for resolution/creation via AGENT_BACKEND env var.
Refactor AgentRuntime to delegate to BackendAdapter instead of
hardcoding Claude CLI. Update GatewayConfig with new env vars
(AGENT_BACKEND, BACKEND_CLI_PATH, BACKEND_MODEL, BACKEND_MAX_TURNS).

Includes 10 property-based test files and unit tests for edge cases.

tests/property/gemini-backend.property.test.ts

@@ -0,0 +1,74 @@
+import { describe, it } from "vitest";
+import fc from "fast-check";
+import { GeminiBackend } from "../../src/backends/gemini-backend.js";
+import type { BackendAdapterConfig } from "../../src/backends/types.js";
+
+// Feature: multi-cli-backend, Property 3: Gemini backend required flags
+// **Validates: Requirements 4.2, 4.3, 4.4**
+
+/**
+ * Arbitrary for non-empty strings that won't break CLI arg parsing.
+ */
+const nonEmptyString = fc.string({ minLength: 1, maxLength: 200 });
+
+function createBackend(): GeminiBackend {
+  const config: BackendAdapterConfig = {
+    cliPath: "gemini",
+    workingDir: "/workspace",
+    queryTimeoutMs: 60000,
+    allowedTools: [],
+    maxTurns: 25,
+  };
+  return new GeminiBackend(config);
+}
+
+describe("Property 3: Gemini backend required flags", () => {
+  it("generated args always contain the prompt as a positional argument", () => {
+    fc.assert(
+      fc.property(
+        nonEmptyString,
+        (prompt) => {
+          const backend = createBackend();
+          const args = backend.buildArgs(prompt);
+
+          // The prompt (or a string containing the prompt) must appear
+          // as a positional arg (not preceded by a flag)
+          return args.some((arg) => arg.includes(prompt));
+        },
+      ),
+      { numRuns: 100 },
+    );
+  });
+
+  it("generated args always contain --output-format json", () => {
+    fc.assert(
+      fc.property(
+        nonEmptyString,
+        (prompt) => {
+          const backend = createBackend();
+          const args = backend.buildArgs(prompt);
+
+          const idx = args.indexOf("--output-format");
+          return idx !== -1 && args[idx + 1] === "json";
+        },
+      ),
+      { numRuns: 100 },
+    );
+  });
+
+  it("generated args always contain --approval-mode yolo", () => {
+    fc.assert(
+      fc.property(
+        nonEmptyString,
+        (prompt) => {
+          const backend = createBackend();
+          const args = backend.buildArgs(prompt);
+
+          const idx = args.indexOf("--approval-mode");
+          return idx !== -1 && args[idx + 1] === "yolo";
+        },
+      ),
+      { numRuns: 100 },
+    );
+  });
+});