Alright, I found the error:

In the TextEdit {} I had inputMethodHints: Qt.ImhNoPredictiveText because in earlier tests, sending emojis to TextEdit crashed the app.

But with PredictiveText disabled, all fancy input methods and hence the different keyboards don't work. Also, Emojis are no problem anymore and animated Gifs are disabled.

In the end everything was fine with the example above.
I just had to update and release my translation files, because in the meantime I changed the name of a .qml file, and the filename is directly linked into the .ts files created by linguist and used by Qt.
I feel a bit ashamed but yes, it was really trivial and kinda stupid :)

You're welcome !

Good to know :)

Since we know now that it's working, please update the thread title prepending [solved] so other forum users may know a solution has been found :)

@SGaist OK. Thanks for the answer. I'll give a try.

@SGaist Fixed it ;)