Google Lens is the most capable of the free, built-in phone tools for handwriting. On clear, print-style writing it is genuinely handy and costs nothing, and for a quick "what does this say" moment it is often all you need.
It falls away on the things this site exists to test: cursive, messy or faded pages, and any kind of volume. There is no batch processing, no API, and only limited export, so it does not scale beyond the occasional note.
Treat it as the free floor. If a tidy note is all you have, start here. If Lens struggles or you have more than a handful of pages, that is the signal to move to a specialist.