SUCCESS!
Hard to find out what's been the essential step. I just booted OxygenOs 10.5.7 this time with a SIM-card inserted and connected to WiFi immediately. Surprisingly now I could enable OEM-unlocking and after that "fastboot oem unlocked" without any issues.
UT 20.04 is running, so the device will be my daily companion from now on.

Thank you so much, mates!

Didn't find out to mark that thread as solved.

@davids
Another path to go. After flashing OxygenOS I've done an offline login procedure, so that might be another chance to try that one more time with wifi connected. Will report the result. Thank you very much.

@MrT10001
Thank you. I will check this. I suppose you suggest having "a valid internet connection" is meant on having that on pc, which I do have via ethernet. I had no SIM-card inserted, so put one in could be another attempt. IMEI ist present.

As my daily driver, a POCO X3 NFC, running UT 20.04, has been damaged, so I went for a refurbished OnePlus Nord N10 (BE2029).

Following the instructions given on the UP homepage I used MSMDownload tool and flashed OxygenOS 10.5.7 on that device successfully. Before that I could unlock the bootloader. After the successful flashing process the bootloader is locked again, so I can't go on any further to install UT on it. Unlocking via adb + fastboot methods won't work, returning "flashing unlock is not allowed". In developer options OEM-unlocking is greyed out and therefore can't be chosen.

On some forums I read the advice to mail to OnePlus itself to receive an unlocking code to re-unlock the bootloader again.

Is there anyone who could help, it would be very appreciated.