How to Fix My SSD Partition with "Unknown Format"

Run

diskutil unmountDisk disk1 (the underlying disk for the container)

sudo fsck_apfs -s -o -y /dev/rdisk3 (the APFS container)

and post the output.

If you are booted from Mojave, run

sudo fsck_apfs -s -o -y /dev/rdisk3

Be aware that going back to High Sierra may be problematic, once we run Mojave on your Mac.

The dd command shows it to be an APFS container. I do not recommend using any third-party software to avoid possible corruption.

Can you run

sudo gdisk -l /dev/disk1

and post the output?

Run

sudo fsck_apfs -n -l /dev/rdisk3

and post the output.

The Paragon APFS for Windows should have a trial. Are you able to read your files, if you install it?

We are going to change the PartitionType GUID of the macOS partition. The 'FFFF' is incorrect, we need to use AF0A. The text in (parentheses) is for informational purposes.

sudo gdisk /dev/disk0

p (Print)

t (Change Partition type)

2 (GPT2)

AF0A (Apple APFS)

p (Print)

w (Write)

y (Yes)

Reboot and test.

Post the output of

sudo dd if=/dev/rdisk1s2 count=5 2>/dev/null | hexdump -C

We need to see the file system headers.

Try

sudo fsck_apfs -y /dev/rdisk3

You will need to unmount the disks.

The disk can be erased to get your disk space back, but you will lose all your data. This is not the ideal situation.

If you have Windows laptop, you can also look at https://www.paragon-software.com/us/home/apfs-windows/#how_it_works and see if you can at least extract all your important non-OS files. If you can, then we can erase/reformat the disk to make ether disk space available.

Mojave allows the use of the -s and -o options, that High Sierra does not. This is from a Mac running Mojave 10.14.6.

fsck_apfs 
usage: fsck_apfs [ [-q | -n | -y] [-l] [-s] [-S] [-o] ] device
       -q            quick check if the superblock and checkpoint superblock are valid.
       -n            verify only (answer "no" to questions)
       -y            always repair (answer "yes" to questions)
       -l            live fsck (lock down for verify-only)
       -s            print space verification summary
       -S            skip iteration of snapshots, although no repairs can be made.
       -o            repair overallocations; please do not run an older fsck_apfs on newer systems with this option

Do you have a copy of the High Sierra installer app? If yes, use an external disk (USB3/TB, because uSB2 would be too slow) and create a HS bootable installer using How to create a bootable installer for macOS - Apple Support. The Mac should be able to boot from this HS installer.

The disk configuration is non-standard. Did you add/replace a second SSD instead of an Optical drive?

Post the output of

sudo gpt -vv -r show /dev/disk1

Can you boot from Mojave and post the output of

diskutil list

diskutil apfs list

If the controller on your Kingston SSD has failed, it is very unlikely that it can be recovered without Kingston's assistance. However, can you post the output of

diskutil list

Your 2011 Mac does not support Mojave as noted in How to upgrade to macOS Mojave - Apple Support. The qualifiers we need do not exist on macOS High Sierra.

Can you try

diskutil repairDisk disk1