I'm updating the situation after some time. Since I installed the battery inside the seatpost with this, I haven't had any more disconnection issues.

I've only been able to use one because I have a D-shaped seatpost.
To "revive" the shifting, I did several tests, and it works both with a mini power bank and with a cell phone + USB-OTG + USBA to USBC.


The day before yesterday, I changed the brake pads and used Shimano L05A ones. To retract the pistons, I removed the screw on the lever side and inserted the cup. Once the pistons were retracted, I removed the cup and closed the system. I didn't have to bleed the system.

I then finally mounted the Shimano 105 11-34 cassette with a CN-HG701 chain. Shifting is perfect. I haven't changed the pulleys yet, as the shifting is excellent even with them. I'm keeping them aside for the future.