Transferring an iMovie project with AirDrop gives "Insufficient Space" repeatedly
I think the following is what actually happens when using AirDrop to transfer an iMovie project from one iOS device to another:


The project is transferred from the sending device into an "iTunes" holding area on the receiving device.  (I'm putting "iTunes" in quotes here, because iTunes the desktop app isn't actually involved in this AirDrop process).
The receiving device then copies the project from there into the main iMovie area.


The issue described in the question occurs when there is enough space to complete step (1), but not step (2).

The "iTunes" holding area can be managed, once you understand this and know what to look for.

On the main iMovie screen (which allows selection between Video / Projects / Theatre), there is an arrow-into-box icon.  This is at top left (iPad) or bottom left (iPhone):



Press the arrow-into-box icon and then select the iTunes tab.  This lists the items available in the "iTunes" holding area I described above.



Projects that failed to complete an AirDrop transfer due to a failure at step 2 are listed here.  This is the cause of the repeated lack of space.

Tapping on an item imports it into iMovie (as in step 2 above), if there is enough space.

Tapping the bin icon allows items to be deleted.  Deleting unwanted items should help to free up enough space to resolve the issue.