@Vlad-Nirky What phone and version did you try it on? On Fairphone 5 24.04-1.1 I can't get the SD to appear.
Interestingly enough, when I have an SD card insertd on my phone and I run dmesg | grep ciborium I repeatedly get udisks2.go:322: Issues while processing /org/freedesktop/UDisks2/block_devices/loop6: interface org.freedesktop.UDisks2.Block not found, while when I don't have it inserted the output is empty.
I can read/write to a USB I had though: I hopped onto my Pi 5 running Ubuntu 24.04 and ran these commands:
sudo umount /dev/sda
sudo mkfs.ext4 /dev/sda
This formatted the drive to ext4, and with an adapter the drive was recognised.
This is what it looks like on the GUI (the very bottom icon is the USB drive, which wouldn't show up if it weren't correctly connected (ie. in such a way to make read/write operations possible):

After performing the same formatting process on an SD card and using an external adapter, it also allowed read/write operations.
I also formatted another SD to FAT format, so UT can handle a variety of formats (probably ExFAT as well for example): it wasn't reading it before, but my other devices weren't either, so it ended up being a problem with the SD (fixable with reformatting in this case) rather than the phone.
It also works with my Samsung T7 SSD, without any need for sudo there for whatever reason.