test(e2e): a localhost connect the machine dropped is tried again on the test side

On a Windows host a burst of test traffic can drop a loopback connect now and then (every port,
any program — measured on the dev desktop). The browser resends it and only waits; Node (libuv)
sends a loopback SYN once and fails at ~300 ms with "connect ETIMEDOUT". `e2e/retryConnect.ts` wraps
Playwright's request context so that one error is tried again (0.5 / 1 / 2 / 4 / 8 s, the system's
own retry waits) while every other failure goes straight to the test; global.setup's health check,
login and /api/me and speed.measure's share probe go through it. Unit-tested; e2e 61/61.

frontend/e2e/retryConnect.ts

@@ -0,0 +1,34 @@
+// Playwright's request context (it runs in Node), trying a connection again when it never came about —
+// as every TCP stack does. Measured on the Windows dev desktop (2026-10-10, the work-group-timesheet
+// suite): now and then, in bursts of 1–15 s, a connect to localhost is dropped — every port, IPv4 and
+// IPv6, any program, no Docker needed; set off by any big test run on the machine. Every other client
+// sends its SYN again and gets in a moment later, but Node (libuv) sends a loopback SYN only once on
+// Windows and fails at ~300 ms with "connect ETIMEDOUT". The request never left this side, so trying it
+// again is safe: the waits the system's own retries take (0.5, 1, 2, 4, 8 s). Anything else — a refused
+// port, a reset, an answer — goes straight to the test. (The browser resends its own SYN: a page only
+// waits, and nothing here can or should hide that.)
+const METHODS = new Set(["get", "post", "put", "patch", "delete", "head", "fetch"]);
+const NO_CONNECTION = /\bconnect ETIMEDOUT\b/;
+const WAITS_MS = [500, 1000, 2000, 4000, 8000];
+
+/** `ctx` with its request methods trying a connect that timed out again (see above). */
+export function retryConnect<T extends object>(ctx: T): T {
+  return new Proxy(ctx, {
+    get(target, key) {
+      const v: unknown = Reflect.get(target, key, target);
+      if (typeof v !== "function") return v;
+      if (typeof key !== "string" || !METHODS.has(key)) return v.bind(target);
+      return async (...args: unknown[]) => {
+        for (let i = 0; ; i++) {
+          try {
+            return await v.apply(target, args);
+          } catch (e) {
+            const wait = WAITS_MS[i];
+            if (wait === undefined || !NO_CONNECTION.test(String((e as Error)?.message))) throw e;
+            await new Promise((r) => setTimeout(r, wait));
+          }
+        }
+      };
+    },
+  });
+}