Thanks to SpiderPig for finding conclusive evidence that this is a bug in MacOS High Sierra - namely, this Reddit thread created within the past few days, which has a few users attesting to it.
For additional context, I thought I'd add the results of my research since asking this question. This particular bug is the latest in a long list of bugs introduced by High Sierra, and is apparently so minor/rare relative to others that it hasn't registered on any of these non-comprehensive lists of them. It has, however, been reported in that last MacRumors thread by myself and at least one another user, so it will hopefully be added to that list soon.
Until Apple eventually releases the update that fixes it, there are two workarounds for this bug.
Convert your flash or external drive to exFAT
You can convert the FAT32 flash drive or external drive that you're having trouble with to exFAT, which is a newer, more superior filesystem with file limits that are so large they can (currently) be considered non-existent.
The only real downside to this solution is that exFAT's relative newness compared to FAT32 will make it incompatible with certain less popular hardware, although it was still released in 2006, so this is increasingly inapplicable. I'd recommend trying to convert to exFAT first and see if the hardware you need to use your flash drive or external disk on supports it. If it does, you're good to go, and if not, you can simply convert back to FAT32.
As far as I'm aware, there's no way to convert to exFAT non-destructively (i.e. without data loss), so you'll need to backup all the data on your drive before formatting the drive in the usual way via Disk Utility, and then transfer your data back once the format is complete.
Use another file manager
This bug doesn't seem so much to be a problem of the APFS filesystem that High Sierra introduced - its replacement to HFS+ - but of Finder itself. For that reason, as oa pointed out in his answer, the bug can also be worked around for now by simply using an alternative file manager like Transmit or Commander One1 until Apple decides to release the fix.
1 Speaking of Commander One, a tangentially related side-note: if, as of the time of posting this answer, you currently have Eltima's Elmedia Player or Folx installed on your Mac, you should follow the instructions here as soon as possible