How to attach virtual (previously additional) classes to blocks?

Apparently, you still think that virtual classes are specifically only classes from other existing blocks - that they exclusively fulfil a single purpose like block classes and global classes do.

That’s not the case. Get rid of that idea.
There are no “real” and “false” virtual classes.

Again, virtual classes can be everything but block and global classes.
They are not necessarily fetched from somewhere else.
You can type in and add whatever you want, right inside the virtual class input field.

And, external classes are not another type of classes, which are just thrown into the virtual classes dropdown.
They are virtual classes.

Why? Because they are neither block classes nor global classes.
Only these 3 types of classes do exist inside the GUI / block inspector.
Also, not sure why you are so obsessed with the naming of the virtual classes.

The class system already has been refactored, after months of discussions and complaints, which went from multiple a day to eventually something around zero.

It seems you are biased, coming from other builders and as soon as something works not 1:1 identically, it just doesn’t make sense to you.
This is alright, unless one is directly questioning the core concept which is working out just fine for tons of users.

For me, it rather feels like you are just sharing your first impressions, which is totally fine.
Still, you have some points, I do admit.

Yes, I do agree here with you. There is room for improvement.
Quick example:

I also find there could be some better organization inside the dropdown, e.g. show/select/filter specific classes/folders, which can be managed via the global and external class manager.

:+1:

Otherwise, the user is forced to type in a class every single time. Some randomly created class is needed. You’d rename the class then anyway to give it a meaningful description?

What’s your suggestion regarding block classes?
You can just delete them and only rely on global classes unless you apply a block style via block inspector.
Just create a global class on your current block and start styling.

Is it necessary to display all existing block classes inside the dropdown of virtual classes?
I think this could be optional (and maybe integrate in a filter functionality I mentioned above).