Power issue - Falsely showing 100% charge

The first issue I had was the laptop was only running on AC, and it was not charging at all. Upon investigation found out, that possibility is my charging cable is bad, because the cable was badly damaged too.

I purchased a replacement charger.

https://www.amazon.com/dp/B07RB2HTB2/ref...

Now that it is charging and showing 100% charged, as soon as I remove the AC, it goes to sleep. When I put AC back on and power back up, it comes back says 5% charge and charging.

My question is do you think it is issue with battery?

Now if this is a battery issue, I have to buy one. As as I was doing research it seems 9350 supports 7.6V battery.

However the aftermarket replacement battery that i could find in ifixit is a 7.4 V battery. Do you think it would work?

Dell XPS 13 9343/9350 Laptop Battery

Thank you in advance!!!