Is my handwriting safe and private on my computer?

Yes. The app's working copies of your notes (both the raw note file and the converted PDF) are stored encrypted on disk, so other apps and people can't read your handwriting out of the cache. Readable copies only appear where you explicitly ask for them — when you save a copy, open one externally, or push a task to another app. And reading from the Supernote is done over your own local Wi-Fi, not the cloud.