filtered is just an array, not a svelte store (or entity that exposes a subsribe() method) so you can't use the $ shorthand to subscribe to it. Just iterate it as an array (without the $).

{#each filtered as pokeman}
  ...
{/each}

But is pokemon a store? if so you'll need to subscribe to it in the reactive statement to see the changes.

<script>
    import Nav from '../components/nav.svelte'
    import {pokemon} from '../stores/pokestore'
    import PokemanCard from "../components/pokemanCard.svelte"

    let searchTerm = "";
    let filtered = [];

    $: if (searchTerm !== $pokemon.searchTerm) {
         searchTerm = $pokemon.searchTerm;
         filtered = filtered($pokemon.pokemons, searchTerm); 
         // *Note: I'm not sure where this 'filtered()' method is coming from but it will conflict with your `filtered` array variable.
       }
 
</script>

<svelte:head>
    <title>Svelte Kit Pokedex</title>
</svelte:head>

<!-- All HTML Work -->
<h1 class="text-4xl text-center m-8 uppercase">SvelteKit Pokedex</h1>
<input type="text" class="w-full rounded-md text-lg p-4 border-2 border-gray-200" placeholder="Search Pokemon" bind:value={searchTerm}>


<style>
</style>


<div class="py-4 grid gap-4 md:grid-cols-2 grid-cols-1">
    {#each filtered as pokeman}
    <PokemanCard pokeman={pokeman} />
    {/each}
</div>

Alternatively you could make use of a svelte derived store for your filtered collection, in which case you would use the $ shorthand in iterating it

<script>
    import { derived } from 'svelte/store';
    import { pokemon } from './stores.js';

    const filtered = derived(
        pokemon,
        $pokemon => $pokemon.pokemons.filter(p => /* your filter logic */ )
    );
</script>

<div class="py-4 grid gap-4 md:grid-cols-2 grid-cols-1">
    {#each $filtered as pokeman}
    <PokemanCard pokeman={pokeman} />
    {/each}
</div>