How to backup PSE 15 (for transfer to new PC) when hard drive is too full?

I'm trying to backup my PSE 15 catalog to an external SSD so I can transfer it to my new PC, which is running PSE 2021. The problem is that PSE 15 tells me that my C: drive is too full to complete the backup. I've optimized/ deleted nearly all of my personal files from the C: drive to make room for this transfer...

....So ironically, it's the PSE 15 data itself that is filling up the lion's share of my hard drive. And I have TONS of room on my external SSD drive.

Is there a way to utilize the ample space on my external SSD to complete this PSE catalog backup? Can I move the C: drive's PSE catalog data to my external SSD, and then initiate the backup? Or is there another way? After gigs and gigs of deletions, my C: drive still has only 10.7 GB remaining, and the majority of the used disk space is being used by PSE 15. Yet PSE15 is telling me that my C: drive is too full to complete the backup. It's a vicious cycle.