Works entirely in Safari

Apple restricts apps that download YouTube content, so App Store tools are limited. yt2mp3.lol runs in mobile Safari — open the YouTube app, tap Share → Copy Link, switch to Safari, paste into the converter, pick MP3 or MP4, and tap Convert.

Saving to the Files app

When the download finishes, Safari will prompt you to save the file. Choose 'Save to Files' and pick a folder on iCloud Drive or On My iPhone. From there the MP3 shows up in any audio app that reads the Files app.

Frequently Asked Questions

No. Everything happens in the browser on a stock iPhone.

Yes — build a Shortcut that takes a shared URL and opens the converter with it pre-filled.