The battery sends basic performance statistics to the OS (Whether it be Linux, Mac or Windows). This is done by a chip in the battery casing.
Sometimes a battery needs to be calibrated by cycling it through using it until it completely drains, then charging the battery up to 100% (Or as near as you can tell) with the notebook computer not being used while charging. I usually suggest letting it drain completely (notebook dies), then plugging it in and letting it charge overnight as you sleep.
A couple of those cycles will calibrate the battery.
Many details as to the battery are set by the manufacturer and accessible in the BIOS (Motherboard) settings, not in the OS.
Some manufacturers include a Reset Button for the battery (I have owned many Acer Aspires and never noticed one) and some manufacturers lock the battery to ensure that the end user only uses OEM batteries and cannot replace it with another maker.
The "energy-full". I checked it with tlp too, and it said:
charge_full= 220 [mAh]
capacity= 5.0 [%]
And if I don't misunderstand anything, then I'm sure that means the full capacity of the battery and I think it should be at least 1000 mAh considering this is the new one. Yesterday when I was testing It said it was on 39% and it said it would need 1 hour to charge to 100% but after a few minutes it was 100% and I unplugged it and it died after like...2-3 mins I think.
I do not think you are misunderstanding anything. Clearly, the battery is giving an improper reading. I would recommend Calibrating the battery as discussed above.
If that does not work, the new battery may actually be faulty.