How to test await block logic in Svelte with Jest - asynchronous

Question

This is my first attempt at writing unit tests for a Svelte app. The below example is based on the standard Svelte template with an additional element added. In this element I conditionally render some text with await block logic.
<script land="ts">
import { asyncthing } from "./asyncthing";
import { onMount } from "svelte";
export let name: string;
let isReady: Promise<boolean> = asyncthing().then((resolveTo) => {
console.log("asyncthing resolved");
return resolveTo;
});
</script>
<main>
<h1 data-testid="greeting">Hello {name}!</h1>
<p>
Visit the Svelte tutorial to learn
how to build Svelte apps.
</p>
<p data-testid="async">
{#await isReady}Awaiting...{:then value}Resolved to: {value}{/await}
</p>
</main>
<style>
main {
text-align: center;
padding: 1em;
max-width: 240px;
margin: 0 auto;
}
h1 {
color: #ff3e00;
text-transform: uppercase;
font-size: 4em;
font-weight: 100;
}
#media (min-width: 640px) {
main {
max-width: none;
}
}
</style>
The function asyncthing returns a Promise<boolean> that resolves after 5 seconds with true.
export const asyncthing = async () => {
console.log("asyncthing() called");
return new Promise<boolean>((resolve) => {
setTimeout(() => {
console.log("timeout expired");
resolve(true);
}, 5000);
});
};
Opening the app in a browser works as expected, but the test below fails.
import App from "./App.svelte";
import { render } from "#testing-library/svelte";
import { tick } from "svelte";
import * as asyncthings from "./asyncthing";
test("messing with async", async () => {
jest.setTimeout(20000);
jest.useFakeTimers();
jest.spyOn(global, "setTimeout");
const asyncthingMock = jest.spyOn(asyncthings, "asyncthing");
const app = render(App, { name: "Everybody" });
expect(app.getByTestId("greeting")).toBeInTheDocument();
expect(app.getByTestId("greeting")).toHaveTextContent("Hello Everybody!");
expect(app.getByTestId("async")).toBeInTheDocument();
expect(app.getByTestId("async")).toHaveTextContent("Awaiting...");
expect(setTimeout).toHaveBeenCalledTimes(1);
expect(setTimeout).toHaveBeenLastCalledWith(expect.any(Function), 5000);
jest.runAllTimers();
await tick();
expect(app.getByTestId("async")).toHaveTextContent("Resolved to: true");
});
The log statements are printed, so the promise does seem to resolve. However, according to Jest the text is not updated. I'm sure I must be doing something wrong, so please, somebody set me straight.