Great project.It's a good idea to use a script to write to a Google Sheets.
In the ideal case for a battery, it is best to use LiFePO4 cells, like 32700. It's much safer than lithium batteries. 32700 has 3.2V and a capacity of about 6500 mAH. It's can supply a current about 30 A.
The adapter is switching and non-linear, and the AC power is not equal to the DC power.
You need to conect VSS to arduino +5v, +9v of battery to VS and you must combine the battery gnd and Arduino gnd pin.