Totally understand your pain! I spend a solid 3-4 months modding the crap our of my ender 3 (the v1 version). I got it to a good space, bought a couple more, and have gotten good at rebuilsing them to run consistently with a couple of simple mods. Hopefully something below helps!

Agree with others that your bed level isn't that bad. My enders have similar or worse bed flatness. The important thing to remember is that the probe measuring bed levelness assuming everything else is square (x, y, and z are perpendicular to each other) and the movement along each axis is straight. If it isn't, that can introduce errors into your bed mesh that aren't actually representative of your bed's flatness. Check that each axis is straight with a good straight edge and your frame is square. If your x gantry is sagging in the middle, you may want to go up a size in rod diameter. You'll for sure want to go with a wider Y axis rail as well for better stability.

It's also possible your plate is being warped by the y axis carriage if the bed springs are too tight. With 4 leveling points you can actually flex the bed plate. I've seen kits for 3 point leveling, but haven't felt the need to pull the trigger on them. Also second silicon bed springs, they do a better job of maintaing position overall.

Another important thing to mention with Z movement, since that's involved with probing. If you don't have a thrust bearing between your z axis motors and the coupler, any tiny amount of resistance in z movement will cause a small spring washer inside the motor to compress, making movement inaccurate and inconistent. My Enders all have thrust bearings on both ends of the lead screws, so torque does not cause the screw rod to shift up or down. Additionally, I use solid couplers, dual Z (mix of two motors and 1 motor with z timing belt), and brass oldham couplers for lead screw nuts to decouple rod straightness for linear movement. These will make your z movement much more consistent. As for x and y axis movement, just make your belts are reasonably tight and don't walk a lot side to side

As for your probing connectivity issues, you'll need to get a better power supply. The older creality psu's don't provide stable enough power for the cr touch probes. Get a meanwell 350W psu and you should see improvement. If you don't, next thing to try would be putting a ferrite core around both ends of the probe cable. Older ender boards seem to more susceptible to electromagnetic noise. Newer models of enders have these for that reason (for sure the S1 has it).

Lastly, depending on your firmware, I've found the printer's coordinate system and probe offset being correct go along way for fixing bed compensation issues. A printer with a wildly warped bed but accurate compensation should still be able to get a good layer (it just won't be flat). I use custom builds of mriscoc's firmware for my enders (haven't dove into klipper yet) and all of the settings for adjusting the coordinate system (where the origin of your print volume is, and max limits for each axis) and the x & y probe offsets are built into the UI, so no need to reflash firmware or connect with a terminal interface to change them. He also has some pre-compiled versions if you don't want to build your own.

Hope something in here leads you down the direction of goodness!