Haven't tried this, but maybe you could create a layout for each post type?

<div class="youtube-post-type">
    @yield('post-content')
</div>

Then use it if the post is a certain type

@if($post['type'] == 'youtube')
    @extends('layouts.youtube-post-type')

No, that part is easy. I'm asking where in database should I store format metadata like youtube links and images ID. What would be the best approach of storing them?

Maybe create a separate metadata table with row post_id, meta_data and type. Then look for rows matching the post_id. This could allow multiple items per post as well.

Yep, that would work and that's exactly how WordPress does it. While it would work fine, I was looking for an alternative approach since I've tried to avoid using a metadata table.