The honest answer first: on iPhone you almost never need an actual MP3. What you want is the sound out of the video, and the format that does the job is M4A. It plays everywhere MP3 does. Pluck pulls it out in about 10 seconds, free.
M4A is the audio format the iPhone speaks natively. It sounds better at the same file size, and it plays on Android, Windows, Mac, and in every browser. Even Apple's own Shortcuts app, the usual built-in answer for this job, hands you an M4A when it converts a video. MP3 on iPhone is honestly a detour.
Sometimes the destination is picky: an old car stereo, a website upload form that only accepts .mp3, a piece of hardware from 2009. In that case, export from Pluck as WAV (the lossless one), then convert on a computer. On a Mac, the Music app makes MP3 versions; on Windows, iTunes does the same. Skip the random converter websites if the recording is personal: your file goes to someone's server, and you have no idea what happens to it there.