How can I see which process does the most writes on a specific partition?

iotop cannot do that because it reads processes IO counters (/proc/PID/io) which are common for all block devices, including virtual filesystems like tmpfs.

What you'll need to do is block I/O tracing:

• https://tunnelix.com/debugging-disk-issues-with-blktrace-blkparse-btrace-and-btt-in-linux-environment/
• https://www.collabora.com/news-and-blog/blog/2017/03/28/linux-block-io-tracing/
• https://www.linux.com/topic/networking/linux-block-io-tracing/

As far as I know there are no ready solutions for that.