The faster Micro 43 bodies (E-M1 mk II, or even E-M1x) with the 100-400 PanaLeica or the forthcoming (and probably expensive) Olympus Pro 150-400 would be a really interesting combination here, especially if a D500 and the 500mm PF Nikkor isn't long enough.
Nikon will get you to 750mm focal length equivalent (1050mm with a 1.4x teleconverter - although that brings the combo to f8 and reduces focus performance) in a somewhat reasonably sized and priced package (a little over $5000 for a D500 and the 500mm lens). Anything longer, and you're in the realm of huge, $10,000 lenses.
Olympus and Panasonic will get you to 800mm equivalent for around $3000, in a much smaller package. I've handled an E-M1 mkII with the 100-400 PanaLeica, and it's not a huge setup at all.
Next year, the Olympus PRO 150-400 lens will be out, which is f4.0 throughout the zoom range (the PanaLeica is, disappointingly, f6.3 at the long end although it's a nice lens in other respects). The Olympus PRO lens is not going to be small or cheap, but it doesn't look any bigger than the Nikkor 500mm PF, although it's hard to tell from the pictures.Since it's f4, it'll take a 2x teleconverter - 1600mm equivalent (at f8, which still autofocuses, although with reduced performance)! It actually has a built-in 1.25x converter, which Olympus claims will stack with the 2x converter and still autofocus, even though it'll be f9.5. Using the built-in converter ONLY, it'll get to 1000 mm equivalent at a very manageable f5.
As far as I know, there's only one way besides the new Olympus PRO lens to get to 2000mm with AF, and it's wildly impractical. It involves the Canon 1200mm f5.6 (the wildly impractical part - it's a 36 lb, $100,000 lens) on an APS-C body. That's 1920mm right there, and a 1.4x converter will fit for 2,688 mm! That's got to be the world's longest AF lens.
If you drop the AF requirement, what qualifies as a lens? I know at least one birder who digiscopes a Celestron 8" telescope with a native focal length over 2000mm (so it's equivalent to a bit over 3000mm with an APS-C camera, or 4000mm or so with Micro 43).
On the same principle, you
could drop a DSLR into the prime focus of the Hale Telescope

, which is a 16,760mm f3.3 lens. As for attaching a camera, there's a Nikon F mount in there somewhere, although adapters to whatever else you might want are the least of the problems (it will also natively attach an 8x10" view camera). It's f3.3, so it'll take at least one teleconverter easily enough. Good luck getting the Hale Telescope off Mount Palomar, let alone to where the birds are