Based on the troubleshooting you've already completed, the issue is likely related to either the Pencil's internal hardware or its battery rather than a software setting.
Regardless, see if the following can help:
- Confirm the Apple Pencil appears under Settings > Bluetooth as Connected.
- Open the Notes app and test writing in a new note.
- If available, test the Apple Pencil on another compatible iPad.
- If possible, test another known-working Apple Pencil on your iPad.
- Check whether the Pencil can still perform actions such as tapping menu items or if there is no response at all.
If the Pencil remains connected and charged but does not register any writing or input on multiple compatible iPads, the Apple Pencil has most likely experienced a hardware failure. Unfortunately, Apple Pencil (1st generation) devices are not serviceable or repairable by Apple, and replacement is typically the recommended solution.