Changing the battery on the keyboard dock or tablet?

I would like to thank you in advance for your support;)

Well, I have a Transformerbook ASUS TX300CA. Unfortunately, the battery now leaves something to be desired. I can only use the Transformerbook without a power supply for 40 minutes before it has to be connected again. Otherwise, I'm still very satisfied, so I don't want to buy a new laptop, I just want to replace the battery.

I found out a little and found out that the keyboard dock and the tablet itself have a battery. I'm now wondering which battery I need to replace. I would also like to know whether it damages the device or the battery if you have it constantly on the power supply during operation. Is it better to remove the laptop from the power adapter and run on the battery after charging, or does it make any difference?

If you describe it like this, the main battery of the tablet has to be replaced by yourself.

Unfortunately, I can't say anything safe about charging myself, since I only use an ASUS notebook. I usually operate this on the power supply, the battery is also permanently installed in the device and can't be easily removed.

The device is 4 years old.