The blue thing is most likely the max speed adjuster.
It looks like the controller is one of those that wraps around the bottom bracket. They're not very common, so i don't know much about them, though there was a thread about another bike that had one. Maybe someone can remember something about it. it was a 202 wheel folding bike IIRC.
The battery wires are doubled up to the pins on the receiver, so two are positive and two negative, but you can just use the outside ones if you want. The batteries often have 4 terminals in them with only two connected anyway.
Without further information, the only thing I can suggest is to test with one of these:
https://www.aliexpress.com/item/60V-3A-DC-High-Precision-Compact-Digital-Adjustable-Switching-Power-Supply-OVP-OCP-OTP-Low-Power/32338416451.html?spm=a2g0s.9042311.0.0.BV1KDd
Set it to 3A and 24v and clip it to the two outer terminals. Test with the wheel off the ground. If the bike works, it's a 24v system. if it doesn't, try 33v. If it works at that, it's 36v.