Those could be for anything. Who knows. They are Deutsch connectors as snt505 stated. Also known as DT connectors. Most aftermarket lighting companies use them such as Rigid, Auxbeam, Zroadz, Diode Dynamics, etc... - Some companies such as Baja Designs use a Weatherpack connector however.
Any triple fog kit you buy will come with a wiring harness you'll use. Most quality kits include a plug and play harness, while some make you provide your own harnesses and figure out the wiring. So I would not be worried about that.
For example, you mentioned doing the Radiance Kit (which is the most popular one that gives you the amber back lighting) which will actually not work with those.
1) The radiance kit has a 3rd wire to control the back light. You only have 2 wires there
2) The radiance lights don't have a plug. It's a cheaper light so they don't put connectors on them. Not to say you COULDN'T make it work. You'd just need to crimp your own connector on the radiance light. But you still have that 3rd control wire to worry about
Check out our Triple Fog Light Kits here if you are in the market. We include wiring harnesses that are essentially plug and play. As I mentioned the Rigid Radiance kits have a 3rd wire but our harness gives you 3 weatherproof connectors you crimp onto the wire which makes it easy/solid/weatherproof. Our Baja and Rigid kits include our harness (which is actually a nice harness and doesn't leave wires dangling/exposed as the previous owner had on your truck). The harness is encased in a protective sheathing.
A few options here
https://www.4x4truckleds.com/vehicl...2017-2018-f-150-raptor/triple-fog-light-kits/
This is the Rigid Radiance Kit:
Or the Baja Deigns Kits (you lose that back light feature but gain a TON of output in light)