It's not a problem that I have dealt with, but I would think that filled up iCloud storage would not affect sharing to file or uploading to You Tube. The latter are functions unrelated to iCloud. Turn off iCloud and try sharing. If the problem still exists then you know that iCloud had nothing to do with it.
In the past I would have suggested updating/upgrading iMovie and operating system to current versions, if you have not already done so. However, if you are not using Catalina, be aware that if you update to Catalina none of your older 32bit apps will work, and your legacy movies will not play in iMovie. Also, the Photos app will update to Photos 5, and there have been lots of issues reported with that version.
So, rather than updating/upgrading any earlier versions that you may be running, the first thing I would try is to reset your iMovie preferences by opening iMovie while holding down the Option and Command keys and selecting 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. Now see if you can share out.
If still no luck, Redownloading iMovie 10 might cure the issue. Drag your present iMovie app from the Applications folder into the trash, but do not empty the trash. Then sign in to the app store and open your purchases folder by clicking on your name at the bottom of the app store side bar. You purchases will be displayed, including iMovie. Update/redownload from there. If for some reason the update is not available or is unsuccessful, then drag your iMovie out of the trash and return it to the Applications folder. However, it should work. Now see if the redownload cures it.
-- Rich