chore: Try fix flakey public processor test (#11348)

Tries fixing a flakey test from the public processor (example failed run
[here](https://github.com/AztecProtocol/aztec-packages/actions/runs/12864214502/job/35862843875#step:3:1373)).
This PR:

- Doubles all times in the flakey unit test, so small variations in CI
affect less
- Adds tests for the public processor and catches the edge case of
timeout being accidentally zero (and thus ignored)
- Removes operations inbetween the timeout being computed and the action
being kicked off

yarn-project/foundation/src/timer/timeout.test.ts

@@ -0,0 +1,20 @@
+import { sleep } from '../sleep/index.js';
+import { executeTimeout } from './timeout.js';
+
+describe('timeout', () => {
+  it('execs within timeout', async () => {
+    await expect(executeTimeout(() => sleep(200).then(() => 'ok'), 300)).resolves.toEqual('ok');
+  });
+
+  it('rejects with custom error on timeout', async () => {
+    await expect(executeTimeout(() => sleep(500), 200, 'Timed out!')).rejects.toThrow('Timed out!');
+  });
+
+  it('rejects if timeout is zero', async () => {
+    await expect(executeTimeout(() => sleep(500), 0, 'Timed out!')).rejects.toThrow('Timed out!');
+  });
+
+  it('rejects if timeout is negative', async () => {
+    await expect(executeTimeout(() => sleep(500), -100, 'Timed out!')).rejects.toThrow('Timed out!');
+  });
+});

yarn-project/foundation/src/timer/timeout.ts

@@ -27,7 +27,7 @@ export class TimeoutTask<T> {
    * @throws An error with a message indicating the function was interrupted due to exceeding the specified timeout.
    */
   public async exec() {
-    const interruptTimeout = !this.timeout ? 0 : setTimeout(this.interrupt, this.timeout);
+    const interruptTimeout = setTimeout(this.interrupt, this.timeout);
     try {
       const start = Date.now();
       const result = await Promise.race<T>([this.fn(), this.interruptPromise]);

yarn-project/simulator/src/public/public_processor.test.ts

@@ -188,12 +188,12 @@ describe('public_processor', () => {
 
       // The simulator will take 400ms to process each tx
       publicTxSimulator.simulate.mockImplementation(async () => {
-        await sleep(400);
+        await sleep(800);
         return mockedEnqueuedCallsResult;
       });
 
-      // We allocate a deadline of 1s, so only one 2 txs should fit
-      const deadline = new Date(Date.now() + 1000);
+      // We allocate a deadline of 2s, so only 2 txs should fit
+      const deadline = new Date(Date.now() + 2000);
       const [processed, failed] = await processor.process(txs, { deadline });
 
       expect(processed.length).toBe(2);

yarn-project/simulator/src/public/public_processor.ts

@@ -372,17 +372,18 @@ export class PublicProcessor implements Traceable {
       return await processFn();
     }
 
+    const txHash = tx.getTxHash().toString();
     const timeout = +deadline - this.dateProvider.now();
+    if (timeout <= 0) {
+      throw new PublicProcessorTimeoutError();
+    }
+
     this.log.debug(`Processing tx ${tx.getTxHash().toString()} within ${timeout}ms`, {
       deadline: deadline.toISOString(),
       now: new Date(this.dateProvider.now()).toISOString(),
-      txHash: tx.getTxHash().toString(),
+      txHash,
     });
 
-    if (timeout < 0) {
-      throw new PublicProcessorTimeoutError();
-    }
-
     return await executeTimeout(
       () => processFn(),
       timeout,