I suspect that your OpenGL libraries are either missing, out of date, or corrupted. Which pretty much covers 100% of what might be wrong without suggesting 1% of how to fix that. I did a search with Synaptic Package Manager and came up with too many hits on OpenGL.
Looking at your lsmod results, they looked surprisingly sparse. This is what I get back:
system@system-p6531p:~$ lsmod | grep nvidia
nvidia_uvm 667648 0
nvidia_drm 45056 4
nvidia_modeset 843776 7 nvidia_drm
nvidia 13119488 458 nvidia_modeset,nvidia_uvm
drm_kms_helper 167936 1 nvidia_drm
drm 356352 7 nvidia_drm,drm_kms_helper
I wonder if something in your Nvidia installation took a dive.
Unfortunately, at this point I've hit the wall. I'm reluctant(!!) to suggest a possible route to reinstall X11, I can't identify what lib's should be reinstalled or installed. I do know X11 and OpenGL should be present with any installation. That you have a GUI desktop says X11 is alive and (presumably) well. If feasable, you could try a fresh Ubuntu installation, and see how Shotcut behaves. This is very much a "throw the spaghetti at the wall, and see what sticks" approach. After that... ya got me.
I think you're better off asking specifically why a launch fails with OpenGL errors.