alternatives for freeing up space on c:

Every trainer has their own ideas of how things ought to be and how things should work. I have never watched any of his videos. My only experience has been that moving things within LrC has made it too easy (for me at least) to drop images and folders in the wrong location and lose them. That is especially true when moving large quantities. I am much more comfortable using the operating system to do that. There are some YouTube trainers I like, and others I don't watch at all.

With those reassurances, I'm now moving folders from c: to an external.

I'm doing this (in the left/navigator panel) by dragging a folder from one drive to a folder on the external drive.

This seems to work, but for the 2nd time,  progress seems to have stopped.  The progress bar for MOVING FOLDER is no longer moving.  Task manager says that LrC is using CPU, but there's nothing in LrC itself to indicate something is happening.  In left panel, the folders formerly on c: are now grey and show "no photos in selected Folder".  But on the external drives folder listing, of the 8 subfolders that were under the parent, only 2 appear and are grey.

Frustrating to see nothing happening!
I had this problem before and closed/relaunched LrC and that seemed to work, but I'd rather know what's going on here

My current thinking is to move some of my image files to an external drive (physical disk), but I worry about performance....I'm assuming that transfer rates to an external drive, even a new one, will be slower than accessing files via an internal bus to an SSL.

I think disk speed where the photos are stored makes only a trivial difference to LrC. Moving photos to an external drive frees up space on your C: drive, and you'll never even notice the change in speed in LrC.

Moving your images to an external hard drive won't impact performance at all. Leave the catalog and other associated files on the C drive. Just move your library of images to the external drive, and everything will be just fine. I have my images distributed across three different external drives and LrC performs just fine. LrC simply needs to know where the images are located. All of the activity takes place in the catalog. As long as the external hard drive is connected so that LrC knows that the images are there, that is all that is necessary. If the occasion arises where you need to leave the external behind you can always create smart previews on the main hard drive to allow you to continue working while the external is disconnected.