How do I get my jots back on a new phone?

Install Jot Minder on the new phone. If you had iCloud backup switched on, a fresh install with nothing in it will pull your backup by itself.

Otherwise, open Settings and choose Restore under whichever service you were using, or Import Backup File… if you have a file.

Everything comes back as it was: your folders, which lists are in them, and the order you arranged them in.