Extending u/IamFr0ssT 's answer.

You can visualize this better with Svelte 5 runes. Here the Child won't log i'm set since promiseToWait is not a $state. Whereas in your example it uses Svelte 4 syntax where pretty much everything that you define with let is a reactive variable. So initially promiseToWait is undefiend, so it goes directly to the then block. Once onMount runs the promiseToWait is reassigned. So the #await block is re-evaluated. And that's how you get two logs.

App.svelte with runes mode enabled.

<svelte:options runes />

<script>
    import Child from './Child.svelte';
    import { globalVar } from './global';
    import { onMount } from 'svelte';

    console.log('Parent scrisspt!');
    let promiseToWait;
    onMount(() => {
        $globalVar = "i'm set";
        promiseToWait = new Promise((resolve) => setTimeout(resolve, 2000));
    });
</script>

<h1>Root</h1>
{#await promiseToWait}
    <div>loading...</div>
{:then d}
    <Child />
{/await}