Is USB 3.0 overkill for Time Machine hard drive?
It depends. I assume your Mac does has USB 3.0 support since you asked the question.

Time Machine target does not need to be very fast, since Time Machine only backup all your files for the first time, it's just delta (changes) it backups after that. So if you delete a file, and create a new file, it backup just those two changes.

But of course the faster the drive, the faster the initial backup.

Media drive don't have to be fast. Even a 1080p video won't exceed like 2MBps, and most USB 2.0 drive can easily go up to 20 ~ 30 MBps (real world)

It's your choice. Again, you need to copy all the files to your external drive, and it takes time.

If they're enclosure, then problem solved. The initial backup and media copy can all be done with the USB 3.0 enclosure, and then just choose which goes to which based on your mood.

My personal experience:

USB 2.0 3.5" 28 MBps

USB 3.0 2.5" 55 MBps

USB 3.0 3.5" 110 MBps

All enclosures, I built them myself!