How to connect iPhone mic to iMovie?

You seem to have done all the correct procedures to connect an external mic to iMovie.

To cover the bases, read my post in the thread linked below where I describe what I did successfully to connect my iPhone external mic--although the situation was a bit different than yours.

iPhone as an external camera? - Apple Community

Since the mic is recognized everywhere but in iMovie, possibly there is a corrupt iMovie preference causing the issue. Try deleting/resetting preferences to see if that triggers recognition of the mic. To delete preferences open iMovie while holding down the Option and Command keys and select to delete preferences in the box that appears. iMovie will open in a new library. Reopen your old library to get back to your projects.  Deleting preferences is a safe procedure that will not cause data loss or disruption to your project.

If the iPhone mic still is not recognized by iMovie, try this procedure:

Resetting

the System Management Controller

Try resetting the System Management

Controller (but no longer available for the new M1 computers):

How to reset the SMC of your Mac - Apple Support

As a workaround you can dictate your audio in the Voice Memos app and then drag the audio file thus created into iMovie.

-- Rich

Hmmmmm. Possibly it is a bug in iMovie 10.3.1 that causes it not to recognize the iPhone mic. I am not able to run iMovie 10.3.1 on my older Mac so regrettably I can't test with my iPhone. Fortunately it does connect with other app on your Mac.

If you need to do an iMovie voiceover, you can use the Voice Memos app on your Mac (in the Applications folder) to make the recording and then drag the recording from the Voice Memos app sidebar onto your desktop and then into iMovie.

-- Rich