Hi all,
I wanted to share my conclusions here so that others might benefit from them as well.
I had to send in the damaged HDD from my NAS for repair. Unfortunately, I didn’t have a replacement HDD (6TB) on hand, so I had to take my NAS offline until I received the replacement.
Unfortunately, it took 4–5 weeks to get a replacement HDD, and that was only because I called three times; according to the salesperson, Western Digital is having trouble processing returned hard drives, so the salesperson sent me a new HDD.
The new HDD was installed, and to avoid having the same problem with it as I did with the previous one in a few months, I “burned in” the hard drive (or at least I tried to).
To do this, I followed the instructions in the old TrueNAS forum: Link
After unfortunately encountering an error with the BadBlock tool several times, I wasn’t sure if it was my own incompetence or if the newly delivered HDD was already damaged 
Well, I contacted customer support again and sent the new HDD back once more. Two weeks later, the new one arrived.
Still hesitant about whether the BadBlocks burn-in tool was really such a good idea, I ran the BadBlocks test on the new HDD again, and 4–5 days later, the test was complete and showed no errors.
Resilvering worked without any problems (as a reminder, I have the 4 HDDs in a split mirror configuration), and everything has been back online ever since.
It seems to me that after replacing the hard drive and resilvering it, the copy speed to the NAS has dropped from about 100 MB/sec to 54 MB/sec. Is that possible? 
Has anyone else experienced this?
Thank you so much for all your support—it really helped me a lot.