I've read a little about external bays, but how are external bays connected to the iMac system?
Any external drive is just a drive in an enclosure with the proper chipset and protocols that allows it to connect to and communicate with the computer. The only difference is you buy one that includes the drive(s) already (external SSDs) or you buy one that you can put your own drive(s) into (external enclosures or docks). The plus side to purchasing just an enclosure is you can get a Thunderbolt 2 version and then add your own SSDs instead of having to worry about an adapter or dock and whether or not the the Thunderbolt 3 drive will work properly through that adapter or dock.
The biggest issue with Thunderbolt 2 enclosures is that it's been quite a few years since Thunderbolt 3 was released, so they're becoming hard to find.
But here is a Thunderbolt 2 enclosure I'm referring to: AKiTiO Thunder2 Quad. It plugs into the iMac directly with a Thunderbolt 2 to Thunderbolt 2 cable and you put your own 2.5" SATA SSDs in the enclosure.
As far as running the drive through the thunderbolt 2 port, if I use the correct adapters such as the Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter that you linked, would that be enough to edit 4k PRORES files?
Possibly, yes. Just keep in mind you're limited to Thunderbolt 2's bandwidth limitations instead of Thunderbolt 3's. So if you buy a Thunderbolt 3 SSD that is faster than the bandwidth limitations of Thunderbolt 2 then you will not get the full speed from that drive.
There are two drives I am looking at on Sweetwater. Both say "USB C compatible," the LaCie claiming "USB-C and USB 3.0 Compatibility." I'm not sure if that simply means that USB-C and TB-3 cables work since they are physically the same.
USB-C is just a connector type. Thunderbolt 3 and USB both use USB-C connectors. What is more important is that you use a certified Thunderbolt cable and that the drive supports Thunderbolt if you want the best performance and reliability.
I'm also not sure what drives you're looking at, but keep in mind what I said in my earlier comment - you have to use drives that are self powered if you want to use the Apple TB3/TB2 adapter or regular Thunderbolt 2 enclosures/drives.