I believe I was successful accessing the SSD using an older Mac as a host with the appropriate Thunderbolt Cable/Adapter. The blackbox requires a Thunderbolt cable not a USB cable. Not all USB-C cables support the Thunderbolt protocol. I know the Apple branded Thunderbolt cables have a lightening bolt on the connector, but I don't know about third party cables and adapters.
When you tried to connect the broken laptop to the 2012 laptop is the 2012 laptop running at least macOS 10.13+ ? It would be best if the laptop was running macOS 10.15, but 10.13 should be enough to see the SSD and the APFS volumes. The M1 Macs have been known to have compatibility issues with some external devices so using an Intel Mac may be better if you want to be sure. Another Intel USB-C Mac may be the best since it may be easier to find a Thunderbolt 3 USB-C Cable to connect the black box to the host Mac.
I was too tired earlier to read the article you linked and did not realize the article did not contain any explicit instructions for connecting the black box to the two Macs. Disconnect the battery flex cable and the BMU battery screw from the battery on the broken laptop. Connect the flex cable of the blackbox to the Life Boat connector on the broken laptop. Orient the cable and the Logic Board as shown in the pictures in the article you linked. Boot the host computer and log in. Make sure the power adapter for the black box is not plugged into the black box. Connect the Thunderbolt cable to the blackbox and to the host Mac. Now connect the power adapter to the black box. Give it a bit of time to mount the SSD of the broken laptop. If the broken laptop has Filevault enabled, it may take several minutes (maybe even five minutes) before you are prompted to unlock the Filevault on the broken laptop. These steps must be done in the order I have described or the SSD on the broken laptop won't ever mount and a cable supporting the Thunderbolt protocol must be used.
If these steps don't work, then you will need to find someone who performs Mac Logic Board repairs and hope they have access to the necessary parts to "fix" the broken laptop so that the SSD can be accessed. There are not very many people who are capable of performing this type of repair. There is a popular and well respected shop in NYC who has lots of board level repairs on YouTube. A professional data recovery service such as Drive Savers may be another option.