Assuming that your Pencil is compatible and was previously working with your iPad, your notes suggest that the Pencil is successfully pairing with your iPad. As such, you can reasonably exclude issues related to pairing and/or Bluetooth communication with the iPad.
This leaves two potential sources of difficulty - these being an issue with the Pencil transducer that interacts with the iPad screen hardware - or iPad software.
If in previous attempts to diagnose difficulties with the Pencil (including changing the replaceable tip) the metal transducer beneath the tip has been damaged, this may very likely be the cause of issues. The transducer element is relatively fragile - and if damaged, may provide inconsistent performance, if it works at all. If the transducer has suffered damage, the only remedy is replacement of the Pencil. Substitution with another Pencil should definitively confirm or exclude a positive diagnosis.
When replacing the Pencil tip, ensure that the replaceable plastic pencil tip is screwed firmly (i.e., finger tight) into the body of the Apple Pencil; even a slightly loosened tip will cause issues. When correctly positioned, there should be a tiny gap (around the full circumference - of about the thickness of a sheet of paper) between the tip and the body of the Pencil.
If you are unable to resolve the problem, a visit to the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) is recommended - where the technicians will be able to test and assess your iPad and Pencil:
Genius Bar Reservation and Apple Support Options - Apple