What could I do to rescue some files from my sm-t320?
If the version of TWRP on your device allows in the Mount section to Enable/Disable MTP, you can use it to connect to your PC and copy files from the internal storage to the PC.

Or you can insert an SD card, and copy files from the internal storage to the SD card using TWRP's terminal with the following command

cp -R /path/to/internal_storage /path/to/sdcard/folder


Then insert the SD card to PC and copy the files.