To power the Xiao board with batteries, you can solder the positive and negative terminals of the batteries to the corresponding battery spots on the back of the Xiao board. Its important to ensure that the batteries you are using are compatible with the board and its charging circuitry. The HAC-006 Li-ion batteries you mentioned have a voltage of 3.7V, which should work well the Xiao board.
When you connect the batteries to the Xiao board, the charging circuitry on the board should handle the charging process when you plug the board into a USB power source. The board should detect the connected batteries and initiate the charging process automatically. Thanks for marking my answer as best.