Default Post post type and custom post type rewrite slugs

So, currently, my blog page is at /blog/ and I also have 2 custom post types. What I’m trying to get is to have all the posts/archives of the Post post type show under /blog/, and for one of the custom post type to use "/" as a rewrite slug. That way, I could get,, which are the custom post types, and if I go to post archive for December of 2020, it would show under /blog/2020/12/.

I’ve tried that, as I said, by setting /blog/%postname%/ under my wp admin permalink settings, and using 'rewrite' => array( 'slug' => '/', 'with_front' => false ), with register_post_type for my custom post type. That works for blog posts, but my custom post type posts show 404, with proper url though.