Hello everybody!
Do we have a running engine here?
YES, WE DO! 
Let me share the full story. I bought a new starter motor, very similar to the original... did it fix the issue? Of course not. But let's start from something I hadn't mentioned before.
As Ruffus wisely pointed out earlier in this thread about buying a used wiring harness:
[...]But be sure it's from the same year. There are sometimes small changes.
He was absolutely right. Here are the differences:

Mine is the wide one (Euro3 spec)
The one they sent me was for Euro4 spec
Had to return it, but I knew the electrical system wasn't the real problem since I eventually got spark.
The focus then shifted to the starter motor. Bought a new one, installed it - but engine speed while cranking remained the same, still not enough for spark. I decided to close the crankcase anyway (stator and coil were good) and tried starting the engine with a drill. That didn't work because the spark plug created too much compression for the drill to handle.
Then I remembered the new battery I bought months ago for this scooter (the type where you need to pour acid in). Installed it and... the cranking speed became incredibly fast, even with the spark plug installed!
This made me question: did I really need a new starter motor? I tested the old one again and confirmed it's at the end of its life - it couldn't turn fast enough to generate spark with the plug in, though it worked without the plug.
What really confused me was that I had done countless tests with car batteries (even with cars running) and never got the starter motor to reach sufficient speed for spark. I suspect my jumper cables were trash and couldn't deliver proper current. They drove me crazy!
Here's a video of the first successful engine start:
https://mega.nz/file/Kt1W2SQa#gQf5CzcMeDIZau8nxoO17c2O9NvzSfiw_-2KuCmK28MTurns out I did need the new starter motor, but it had the positive terminal in a different position compared to the original. As you can hear in the video, I couldn't install the airbox because of this.

My solution was to take both starters apart and swap the internals of the new one into the old housing:

Later I discovered this wasn't even necessary - you can just loosen the two screws holding the starter together and rotate the cylinder slightly. Who knew!
But wait, there's more! After the first test ride, I noticed the ABS activates immediately when using the rear brake (doesn't happen with the front). Removing the ABS fuse returns the rear brake to normal operation (without ABS intervention).
Any suggestions? My first step will be cleaning the ABS sensor (which means removing the muffler again

).
Thank you all for being part of this journey. I couldn't have done it without this community's help.