Since your Bluetooth is connected, the LED works, and the tail button functions, that means:
Bluetooth pairing is OK
Battery and charging are OK
Button electronics are working As the Pen tip is not writing → this usually means either:
Pen tip hardware issue
Touch driver issue
Wrong pen compatibility
Digitizer driver problem
Settings → Windows Update → Advanced Options
Click Optional Updates
Install all Surface firmware updates
Shut down Surface completely
Press & hold Volume Up
Press Power
Release Power, keep holding Volume Up
You enter UEFI screen
Try writing there.
If pen works → Windows driver problem
If pen does NOT work → Pen tip hardware problem