I dont know if this qualifies as a “toaster” but Ive used this docking bay in the past for a NAS and it served my purposes decently well. One thing to keep in mind is that random IO will be lacking with a usb interface. Also, this particular chipset does powercycle all the drives when one is removed so drive swaps end up requiring you to power the entire system off to perform. Also no integrated cooling may be a deal breaker as you illuded to.
If I was basing a nas build off of a PI, I would look to use the PCIe 1x2.0 interface on the pi 5 as a HBA.
Just to make sure. Are you copying to your ZFS pool directory or a dataset? Check to male sure your paths are correct.
Push vs pull shouldn’t matter but I’ve always done push.
If your zpool is not accessible anymore after a transfer then there is a low-level problem here as it shouldn’t just disappear.
I would installe tmux on your ZFS system and have a window with htop running, dmesg, and zpool status running to check your system while you copy files. Something that severe should become self evedent pretty quickly.