Some Custom Content Types cannot be added to lists or libraries / not showing

I am creating custom content types in the "content type gallery" on the ContentTypeHub site. Previous custom content types are available in my other SharePoint sites, but new ones cannot be added. I can see them in List Settings > Add Content Types, but not in List > Add New Column > Content Type. I cannot add them via either menu, in modern or classic view. Some of these are a week old, so it's not that they aren't available yet (and new ones show straight away on the List Settings > Add Content Types menu, where you can no longer add content types).

I am stumped as to what the problem is. The issue persists for Libraries too and across different content types.

Edit to make it clearer (as this was a common reason I've seen online):
The Parent of the content types I want to add to lists are "Item".
The Parent of the content types I want to add to libraries are "Document".

I have just checked on another site and they are showing there, but not on the one I need them on.