In my case, there was a (keyboard?) ribbon cable glued/stuck to the bottom of the battery.

I had to carefully lift it at an angle a blast it with a hair dryer for a while until it loosened.

I struggled with back cover removal. Eventually I've managed to insert the tool between the sim-tray slot and the screen. Just be careful not to break the thin section of plastic.

The battery itself was also harder to remove than expected. The original adhesive is quite strong and the angle you have to pull at is pretty bad.

In the end I was able to complete the battery swap. Thank you for the guide.