If got a new computer without an internal floppy drive, but I do have an external floppy drive.
When I connect it, it is seen as a "disk" and not recognized as floppy drive.
How can I get Linux to recognize an external usb floppy drive as floppy?

It doesn't matter what it's called, as long as it works. Presumably it is using the "usb-storage" driver and you can pretend it's a very small HD. You just have to take care to explicitly invoke the correct tools for creating a filesystem on it, just so you don't waste a lot of space for inodes. If you can mount and read a floppy, that is a good indication that the device will behave as you expect, despite the name.

Okay. But it is not the name I care about. Other programs should see the drive as floppy, e.g. Startup-manager, to write a boot disk.

Because it is usb floppy drive and not internal it will always be detected as sdb or something similar.
This is because you have not connected it to the floppy connector inside the box.
If you want, once the floppy is mounted automatically, you can unmount it and remount it where you would like to. But as said before, where it gets mounted really makes no difference as far as it is working properly for you the way you want it.
Other way is to edit fstab file to auto mount it where you want at boot if you have it connected all the time.

So, if I edit the fstab file with

/dev/sdc /media/floppy (and the rest)

I should be okay?

(I use sdc here because I have 2 drives inside my computer).

I shall try that later on.
Thanks. I'll let you know if it works.

I could mount "the drive" as floppy, but as soon as I put a floppy in it, it again mounts the floppy as disk. (?!?@?)

It will mount it as disk because of the reason that it is usb connected and anything that is connected to usb is usually mounted on disk.
You can still unmount it without hampering its operation.

Okay. Thank you.

Anyway, I replaced the media card reader with an internal floppy drive.
So the issue is not an issue any more.