fix(perf): actually produce a React profiling build

DevTools still reported "Profiling not supported" because the build was never a
profiling one, despite three settings appearing to enable it. Next applies the React
swap through a webpack alias — getReactProfilingInProduction, mapping
'react-dom/client$' to 'react-dom/profiling' — that Turbopack never sees. A Turbopack
resolveAlias does not catch it either: the vendored entry requires
./cjs/react-dom-client.production.js relatively, not through a bare specifier.

The Dockerfile now performs that same swap on the vendored entry when
HOMARR_PROFILING=true, guarded so it fails the build loudly if React's file layout
changes rather than silently producing a normal build again.

Added `pnpm docker:profiling`, which builds and then verifies, because
`docker build . -t homarr:performance` alone yields a non-profiling image and that is
almost certainly what was being run.

verify-react-profiling.mts checks the bundle rather than the runtime: 2 client chunks
carry React's profiling renderer with the flag, 0 without. It replaces a Playwright
probe that could not tell the two apart — React sends a reduced inject payload to a
synthetic devtools hook, byte-identical for both builds, so that probe reported a
false negative for profiling and production alike. The bundle marker discriminates;
confirm the Profiler tab itself with the real extension.

scripts/benchmarks/verify-react-profiling.mts

@@ -0,0 +1,51 @@
+/**
+ * Verifies a built image actually ships React's *profiling* renderer, which is what
+ * React DevTools needs before it will enable the Profiler tab instead of reporting
+ * "Profiling support requires either a development or profiling build of React".
+ *
+ *   node --experimental-strip-types scripts/benchmarks/verify-react-profiling.mts homarr:performance
+ *
+ * Why a bundle check and not a runtime one: DevTools decides from the renderer object
+ * React passes to `__REACT_DEVTOOLS_GLOBAL_HOOK__.inject()`, but a synthetic hook makes
+ * React send a reduced payload that is byte-identical for profiling and production
+ * builds — so a Playwright probe cannot tell them apart and gives a false negative.
+ * The marker below can: it exists only in React's profiling bundle.
+ */
+import { execFile } from "node:child_process";
+import { promisify } from "node:util";
+
+const execFileAsync = promisify(execFile);
+
+const image = process.argv[2];
+if (!image) throw new Error("usage: verify-react-profiling.mts <docker-image>");
+
+/** Present in react-dom-profiling.profiling.js, absent from react-dom-client.production.js. */
+const PROFILING_MARKER = "TracingMarker";
+
+const run = async (script: string) => {
+  const { stdout } = await execFileAsync("docker", ["run", "--rm", "--entrypoint", "sh", image, "-c", script], {
+    maxBuffer: 16 * 1024 * 1024,
+  });
+  return stdout.trim();
+};
+
+const clientChunks = Number(
+  await run(`grep -rl "${PROFILING_MARKER}" /app/apps/nextjs/.next/static/chunks 2>/dev/null | wc -l`),
+);
+const vendoredEntry = await run(
+  `grep -o "react-dom-[a-z.]*\\.js" /app/node_modules/next/dist/compiled/react-dom/client.js 2>/dev/null | tail -1 || echo "(entry not present in runtime image)"`,
+);
+const sourceMaps = Number(await run(`find /app/apps/nextjs/.next/static -name "*.map" 2>/dev/null | wc -l`));
+
+console.log(`image:                    ${image}`);
+console.log(`client chunks with React profiling renderer: ${clientChunks}`);
+console.log(`vendored react-dom client entry points at:   ${vendoredEntry}`);
+console.log(`browser source maps:      ${sourceMaps}`);
+
+const ok = clientChunks > 0;
+console.log(
+  ok
+    ? "\nPROFILING BUILD CONFIRMED — React's profiling renderer is in the client bundle"
+    : "\nNOT A PROFILING BUILD — rebuild with: docker build --build-arg HOMARR_PROFILING=true .",
+);
+if (!ok) process.exitCode = 1;