Upload to UNO R3 connected via USBIP fails: "programmer is not responding"

v_mark:
If only somebody (who knows Arduino IDE well) could confirm that I lost "only" a kind of safety net, so I will recognise harder if my code somehow will not uploaded...

It's the verification step that's failing. That's where it reads the uploaded binary back from the microcontroller's flash memory and compares it to the .hex file on your hard drive. Verification is intended to alert you if the data was somehow corrupted during the upload. After reading tens of thousands of posts on the forum over the last 7 years, I don't remember a case of the verification catching a legitimate problem, so I don't think it's a big deal if it's not working for you. You can turn it off in the Arduino IDE at File > Preferences > Verify code after upload.