On the mini your bed leveling is going to be connected to the Z-min end-stop spot on the board. The red goes to the nozzle and black to the bed.
The blue and black cable you have unplugged in your picture is for the physical Z-min switch. The minis 1.03 and below have this installed on the left Z carriage but the minis 1.04 and above do not.
I noticed one thing that’s unrelated to this issue but could cause issues in the future. You’re heat-sink is slipping down and getting close to shorting out some componants on the board. If you remove that you can prevent some future issues.
I agree with kmanley that your main issue is going to be from the nozzle to the screw. If there isn’t continuity there you’re not going anywhere. You mentioned taking off the nozzle to get to a clog. It’s possible but I don’t think too likely that there is some plastic in between the nozzle threads and heater block insulating the electrical connection between the two.
It’s also possible that there’s a small film of basically invisible plastic on the outside of the nozzle insulating it. I’ve experienced this mostly when printing with Nylon. Even after doing cold pulls with Nylon I’ll have issues with auto-leveling until I clean the outside of the nozzle really well.
Would you mind giving the out-side of the nozzle a good cleaning with a scotch brite pad, or something else abrasive but non-conductive? Try heating the nozzle up to the extrusion temperature of the last plastic you were printing with when wiping down the nozzle. This is what I’ve found helps most with getting Nylon cleaned off. Using this higher temperature than the normal wipe routine can do the trick in these cases.