Do you have SAN/NAS devices connected to these servers?
As a first step, I would recommend uncheck the "1-Touch recovery" option so as to continue protecting your servers with your daily incremental FS backups via the File System Agent. This will ensure your postbackup phase will not run, and your backups complete, albeit without the ability to recover using 1-Touch.
Since you mention "lsblk" was also stuck, that indicates this issue is related to one or more disks having I/O errors. i.e. partinfo stalled for the same reason as the OS utility "lsblk" stalled.
You can use this script to identify the problematic device. note that the command will get stuck, but should have printed the device name before it gets stuck, so you can identify the problematic disk and take necessary action.
# for dv in `ls /sys/block`; do echo "check $dv"; lsblk /dev/$dv; echo ""; done