MacBook Not Booting: Disk2s4 Partition Won’t Mount

About 7 months ago my 16inch MacBook Pro 2019 broke due to water damage. I initially brought it into a local repair shop, but they were unable to fix it. After this the MacBook sat dormant for about 6 months before I decided to try again and send it in to a more reputable repair shop that has successfully fixed my devices in the past. They were able to get the MacBook working, but warned me that the previous repair shop had refluxed some of the components, including the SSD, and that this might compromise the stability of my system. When I received the device back from the repair shop, it worked perfectly fine for about a day. The next night I accidentally fell asleep while watching youtube videos which lead to the devices battery being drained. Upon recharging it the next morning and trying to turn it on, I was met with a screen which displayed a folder with a question mark icon and a reference to the startup section of the apple support site. I assumed this meant the MacBook was unable to read my boot drive, so I restarted the device in recovery mode. When opening disk utility, it shows that my main drive is recognized, but only the recovery and data partitions are mounted, with the system volume (labeled disk2s4) being unmounted. When trying to mount disk2s4, either using the disk utility or the terminal I get the error “failed to read superblock”. Running first aid on disk2s4 or any of the other partitions also fails. Trying to unlock the partition doesn’t do anything as it wasn’t encrypted in the first place. I want to try reformatting and reinstalling the OS onto the system volume (disk2s4) partition but before I do that I want to backup my data (I would exclude any system files as to mitigate the chances of reintroducing the issue).

I can browse through my personal files in the terminal, and everything seems to be there so I believe my data should still be intact. Initially I was going to just use rsync, but out of fear it may miss some files and/or cause complications when trying to restore, i’ve decided to see if I can use time machine instead. I’ve tried making a bootable environment on my external drive to hopefully get access to my data and make a time machine backup, but I ran into issues when trying to allow booting from an external drive in my Startup System Security settings, getting an error stating that no admin exists. Before trying to resolve the issue in the terminal I decided to give target mode a try. But because I don’t have a thunderbolt cable, i tried using a USB-a 3.0 to USB-C connector, plugged into an Anker usb hub on my older MacBook Pro (also running MacOS 11). This just gave me an error stating that the drive is incompatible and asking me to either eject, ignore, or initialize. I thought that this might be due to the fact that i’m using a pretty janky method to connect the computers so I ordered a thunderbolt cable online and it should arrive later today. I’m not super confident that using a thunderbolt cable will make a difference, so I’m making this post preemptively.

As I am very inexperienced when it comes to the inner workings of MacOS, I was hoping someone more knowledgeable could provide some insight into my situation. Is rsync a viable option for backing up and restoring my data? Is there a different way to boot to an external drive or fix the “no admin exists” error when trying to change Startup System Security settings? How could I possibly solve the incompatible disk problem when using target mode? (if just using a thunderbolt cable doesn’t end up solving the issue).

Any suggestions, references or solutions would be extremely helpful!