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If I look at the images of the Specialized Diverge Elite E5 I see on the underside of the seat stay 2 black pieces that look like rack mounts.
However, I've only seen them on the upper side of the seat stay. Are they pannier rack mounts or something else? If they are rack mount, how can I connect a rack to them? Is there a reason to add those to the bottom? Does that somehow improve something?
They are fender mounts. A bridge is connected to those mounts, and an L-bracket connects the bridge to the fender.
As for pannier rack, there are fenders that carry lightweight panniers, such as Hebie Wingee. If you want to carry more than 8 kg per side, then you need a real pannier rack. It needs mounts at the bottom and at the top of the seat stays. Usually those under-the-seatstay mounting holes don't work because regular pannier racks are intended to be mounted to eyelets that have the screw holes at the sides of the seatstay. Theoretically you could fabricate custom mounts for those under-the-seatstay holes, though.
Quoting this website from Specialized:
To keep the frame as streamlined as possible, the rack's upper mounts attach to a specially designed seatpost collar that is included with all non-EVO bikes (S204700001). [emphasis mine]
https://www.specialized.com/gb/en/specialized-rear-rack-seat-collar/p/133425?color=219604-133425
Furthermore:
A removable chainstay bridge is included with all models for an additional fender mount (S209900019).
Note that this appears to be a typo from Specialized, as the part is meant for the seat stays, not the chain stays.
There are many designs of rack - some bolt to the seatpost but are limited in their load capacity.
Another option is something that has long spindly straps that can be freely bent to suit your bike. However this sort will absolutely need rack mounting holes in your frame, down by the rear dropouts in order to hold the load's weight vertically. For example:
You can also use P clips around the seat stays if the frame's holes are unworkable:
Or you can use a clamp around the seatpost to provide some mounting holes.
Regardless of how you do it, the rack needs a minimum of three contacts with the bike, and four is better again.
On the plus side, the rack can also act as a partial mudguard and a good place for mounting a large reflector/light.
There are pannier racks like the Thule Tour Rack that don’t bolt on and instead clamp directly to the seat stay. You may be stuck with proprietary panniers with a system like that.
Alternatively you could run a bikepacking style seat pack. A little limited in capacity (< 15L) but a possibility depending on your needs.
