Timemachine freezes

I have a WD My Book (4TB with less than 1GB used), and I am trying to back up my MacBook 2018.

I've used this same external HDD to backup my files from my iMac, and everything works like a charm. The issue happens when I connect and try to backup my Macbook on this HDD. The process starts smoothly, the data gets encrypted and starts copying to the HDD. The process goes well up to 50~60% (this number varies). At this moment it gets stuck in a % between these values (last time was 53.4%) and the time machine screen freezes, my spotlight stops showing me application options (if I try to open anything else), and the backup does not go any further.

The HDD becomes inaccessible (I have an extra partition there with files). I've initially suspected the adaptor I was using to go from USB to USB-C and got another cable online, but I am incurring in the same failure mode. The HDD is not faulty because I can directly use it to back up my iMac and it works like a charm, with no issues.

Is there anything I could do, to make my backup work?