perf(engine): a --gpu render probes the GPU encoders once, not twice (#6638)

* perf(engine,cli): a machine's GPU encoder probe runs once, not on every render

* refactor(engine): one shared probe per process, no answer kept on disk

packages/engine/src/utils/gpuEncoder.test.ts

@@ -1,10 +1,12 @@
 import { afterEach, describe, expect, it, vi } from "vitest";
 
 import {
+  getCachedGpuEncoder,
   getCompiledGpuEncoders,
   getGpuEncoderName,
   getProbeArgs,
   mapPresetForGpuEncoder,
+  resetCachedGpuEncoder,
   selectUsableGpuEncoder,
 } from "./gpuEncoder.js";
 
@@ -146,3 +148,12 @@ describe("getProbeArgs", () => {
     expect(args[args.indexOf("-allow_sw") + 1]).toBe("1");
   });
 });
+
+describe("getCachedGpuEncoder", () => {
+  afterEach(() => resetCachedGpuEncoder());
+
+  it("is one probe however many callers ask while it runs", () => {
+    const first = getCachedGpuEncoder();
+    expect(getCachedGpuEncoder()).toBe(first);
+  });
+});