User Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:66.0) Gecko/20100101 Firefox/66.0

Steps to reproduce:

Drag and Drop a .jpg picture into the composition pane. (= not as an attachment)
Send this email.

Actual results:

Everything seems fine on my side, but the recipient won't receive the inline picture (no correlation to certain provider, neither on my or the recipients side).

Expected results:

The recipient should see the inline pictures.

Can you send a test message with a (small) picture and check the message in the Sent folder. Is the image present?

Oops, as I'm writing this, it's dawning on me. You've got an option set to force your e-mail to plaintext and you lose the images. See bug 1510134 and its duplicates.

Yeah, I had this in mind as well. But my option is set to "automatic".
Which indicates that the so called "automatism" is nuts.
We should either fix it, or remove it.

You should also check the recipient settings in the address book.

All of them say "unknown".

OK, if the recipients say "unknown", then most likely you have this option set:
Tools > Options, Composition, General (tab), Send Options (button):

When sending messages in HTML format and one or more recipients are not listed as being able to receive HTML:
Convert the message to plain text.

Since your recipients say "unknown", the plain-text conversion will be forced.