New to maintaining cycles. Need help repairing a broken freewheel for a Cube MTB.

The part number is Shimano HG CS-HG51-8an.

I noticed for a while the pedals were skipping. I thought it might be the chain or the sprockets. At the time I got this bike I had it serviced at a shop, but the issue persisted.

The bike would skip when I was starting from rest or in generally high torque situations. Finally it got to a point where the pedals wouldn't transmit any torque to the wheels.

I'm really new to repairing bikes. I tried looking up replacement parts, but I'm always afraid of compatibility issues, whether I'm buying the right tool/part etc. I'm really starting from scratch.

Currently I'm in Denmark, if that helps. Please let me know if there are any missing details that would be helpful.

Here's what I've found…
https://cykelgear.dk/vaerktoj/vaerktoj-til-kassette/pathtaker-aftraekker-til-shimano-hg-kassettecenterlock-lasering

https://www.cykelpartner.dk/kassettehus/kassettehus-shimano-non-series-til-89-gear-fh-rm6670

Thanks for the help!