I was on v2 of wrangler. Upgrading to v3 solved the issue. Thanks a lot.

Queue test-queue (5 messages) - Exceeded CPU Limit @ 30/05/2024, 19:52:42

Queue test-queue (5 messages) - Exceeded CPU Limit @ 30/05/2024, 19:52:42

app.get("/test", async c => {
    const message = `Test message. Random number: ${Math.floor(Math.random() * 100)}`;
    await c.env.WEBSITE_QUEUE.send({
        body: message,
    });

    return c.json({ success: `Queued up this message: ${message}` });
});

app.get("/test", async c => {
    const message = `Test message. Random number: ${Math.floor(Math.random() * 100)}`;
    await c.env.WEBSITE_QUEUE.send({
        body: message,
    });

    return c.json({ success: `Queued up this message: ${message}` });
});

export default {
    fetch: app.fetch,
    async queue(batch: MessageBatch<{ body: string }>, env: Environment) {
        for (const message of batch.messages) {
            console.log(
                `Consuming message: ${JSON.stringify(message.body, null, 2)}`
            );
        }
    },
};

export default {
    fetch: app.fetch,
    async queue(batch: MessageBatch<{ body: string }>, env: Environment) {
        for (const message of batch.messages) {
            console.log(
                `Consuming message: ${JSON.stringify(message.body, null, 2)}`
            );
        }
    },
};