A knock wood update:
Since I decomissioned both of my USB-C external drives (one exclusively for Photos, the other for Time Machine backups), I haven't had any kernal panics. None.
As I mentioned above, I am currently using an old Seagate USB 2.0 drive to do Time Machine's dirty work. It backs up hourly with no issues, and in under a minute and a half generally. In other words, it works.
This is, in my opinion, Apple's buggy implementation of USB-C in Sequoia/Sonoma. (Upon reflection, the Time Machine backups taking way too long may have begun in Sonoma.) Likely a software implementation issue, in my opinion. They need to fix this ASAP. (And yes, I have reported the issue to Apple.)