After fixing the battery charging circuit, it worked as expected, but the LM317 got quite hot. Also right now my design uses both lithium cell in series without balance charging. This imposes some avoidable safety risks. Also, because of the lack of diodes, the battery would slowly discharge over the adjustment resistors of the LM317.

Because of all that I decided to redesign the charge circuit. The plan now includes two LM317s, one for each cell, protective diodes and a voltage device to make the ESP monitor the battery.