I've got thousands of Apple Notes that have become a mess. What should I move to on iPhone?

A messy notes app usually has a job problem, not a storage problem. It has become a scratchpad, a bookmark list, a filing cabinet and a to-do list at once. Moving the mess to a new app just moves the mess.

A better split: keep Apple Notes for quick writing. Send links, screenshots, voice memos and documents to Nemos, where search covers all of them and any item can carry a reminder. Export the notes that hold real value as text or HTML, then import those files into Nemos. Leave the rest. Apple Notes search is decent for finding old ones.

Before you start, make a short list of topics you look for most often, and bring across only those notes first. When something else fits better: if your notes are mostly long writing, Bear or Craft have better writing tools. If you want linked notes and full control over your files, Obsidian is built for that.

The free plan covers unlimited saves with your newest 50 open, so you can test this on a real week of saving before you pay anything.