get_permalink( $post->ID ) returns plain permalink instead of pretty permalink for CPT registered on subsite

[1theo]

I have a multisite network with CPTs that are registered individually by subsite.
The main site provides an overview of these, using

get_permalink( $post->ID );

to link to the pretty permalink location in each subsite.

After the introduction of

wp_force_plain_post_permalink()

in WP 5.7.0

#52373 #5272

get_permalink() returns plain permalinks due to failing to pass the test in wp_force_plain_post_permalink():

	$post_type_obj   = get_post_type_object( get_post_type( $post ) );

get_post_type_object() returns null, as the CPT is not present in the global $wp_post_types of the main site (even after trying switch_to_blog( $post->blog_id );