Prohibitory symbol on MacBook Air and recovery will not work

I recently asked a question about 2 bricked SSD drives in my 2013 MacBook Air’s.

I tested the Air’s using a 3rd working air’s SSD. they both booted up fine with the working SSD and I was able to login. I re-installed the working SSD back into the 3rd Air and now I receive the prohibitory symbol.

I attempted to run a recovery on the drive: Command + R keys and it brought me to the recovery window however it was attempting to install Yosemite (what the mac was shipped with) the Mac was running High Sierra before this issue. I went into recovery mode using key combination Option + Command + R keys to install the latest OS-X and gain access back to the Mac with hopefully my data still there.

It went through the process and went to install but the disk was not available to install on. I went into disk utility and tried to run a repair and it failed. the disk cannot be mounted either.

I used a MacBook Pro, running Catalina, and placed my Air into Target Disk Mode, the Air went into Target Mode but the drive is not showing up on the MacBook Pro (host).

I’m at a loss! I don’t want to lose my data, it is pictures of my children and some of my wedding. At this point I don’t know if the drive will let me format it even if that was my last option. Not sure why removing a drive for testing and reinstalling bricked another proprietary 2013-2015 Apple SSD.