I don't have a fixed budget, but somewhere around £5K. Total weight around 2kg +/- 10%. Zoom lens is more flexible, but not averse to prime (esp as typically works better with TC). I have experience of both m43 and FF and happy to consider any format.
I'm guessing on what £5K will get you, as I have to convert it to USD - which is about $5800 - but you also don't have to deal with the Taco Tariffs, so that £5K should go further than $5800 does in the US (I think) unless you're in a country that photography gear comes at a premium.
Even though I'm a Sony guy (for now, anyway), I'd look at Canon, and specifically at the RF 100-500mm f4.5-7.1 lens. It's relatively lightweight - lighter than the Sony 200-600mm and Nikon 180-600mm - and should keep you at around the 2kg goal, whereas those others won't, and has the zoom advantage over both companies' 100-400mm lenses. Actually, with any of the good Canon bdeies, it's a lighter combo than the Sony 100-400mm with any of their full frame bodies (and probably Nikon as well, but haven't looked). The Canon RF 100-500mm also takes the 1.4x TC pretty well from what I've seen, at least when you have good light (the TC drops f7.1 to f10).
You have a few choices with Canon bodies. A couple of the choices will require some patience.
1. R6 Mk II. 24mp and fast burst and readout speeds.
2. R6 Mk III. Supposedly to be announced very soon. Price with the 100-500mm may or may not put you over your budget.
3. R5 (first version). The Mk II is probably beyond your budget. The Mk II has obvious advantages over the first version, but the first R5 actually has some IQ advantage over the Mk II. The Mk II has a stacked sensor that allows for faster bursts and has a faster readout speed for less rolling shutter issues, but the stacked sensor doesn't handle noise as well as the older sensor on the first R5.
4. R7 Mk II. Don't bother with the first one. The Mk II is rumored - most definitely in development, but so far we haven't heard much definitively about its specs or features. One rumor is that it won't have a mechanical shutter, which implies the readout speed (slow on the R7 Mk I) is fast enough that a mechanical shutter isn't needed. Another rumor is that it doesn't have a stacked sensor, which seems contradictory to being fast enough to not need a mechanical shutter. However, if they can boost the readout speed, it might indeed not need to be a stacked sensor. The R7 already has a pretty fast burst speed (but a small buffer) with an unstacked sensor, so even if they don't make the burst faster, as long as the readout speed is faster we should be golden. We're also hoping it has a larger buffer, maybe a CFe card slot, and other improvements. The R7/R7 Mk II has an APS-C censor with a 1.6x crop factor, which has its disadvantages and advantages. I'm sure you know the disadvantages are, so I won't bother listing them. The 1.6x crop gives you a 160-800mm effective field of view, without the need for the teleconvertor and without the 1 stop hit to your aperture. A lot of Canon people that shoot with R6 and R5s also bought an R7 for this reason.
If you're not interested in the R7 Mk II, that leaves us with the question you had about 24mp + 1.4x TC vs 45mp. This does get tricky because while the obvious answer might seem to be the R5 since you can always add the 1.4x TC to that body as well. However, the R5 is a slower camera than the R6 Mk II (and presumably the Mk III). Between the R5 and R6 Mk II, I'd lean towards the R5, but I think you should wait for the Mk III announcement (and availability) before making that decision.
Your options with Sony are somewhat limited. There's 2 3rd party 500mm lenses, the Tamron 150-500mm and Sigma 500mm f5.6 prime. However, the bodies available don't quite compare to the Canon options. For faster framerates you have to go with either the A9 or A1, as the A7 bodies don't get anywhere near what Canons have. The original A9 is affordable, but it's old. The A9 II is probably outside your budget when you add a lens, as is the original A1. The lightweight Sony lens option is the 100-400mm GM with the 1.4x TC. If you don't need the faster burst speeds, the A7IV is the current midrange option, but it's a bit old, and the A7V is due to be released soon. The Tamron 150-500mm is an average lens, good but not great (watch the reviews). The Sigma 500mm is small and light for what you get, and is one of the sharpest lenses you can buy without paying used car prices.
Another Sony option is the a6700 (like I have), with a myriad of lens options. There's the 70-350mm (105-525mm - actually more like 535mm effective field of view because the crop is actually 1.53x), which is very small and light for what you get, the Tamron 50-400mm (114-612mm), and the Sony 100-400mm GM (153-612mm) that also takes the 1.4x TC well. The 15fps limit that Sony imposes on 3rd party lenses is moot with the a6700 (actually all Sonys other than the A1 and A9 line). The autofocus on the a6700 is absolutely amazing. However the smallish, side-mounted viewfinder might be a deal killer.
Nikon has a compelling option with the Z6 III and the 400mm f4.5. It's small and light, sharp, and the Z6 III is a pretty amazing camera for the price. It's shorter than the 500mm you want, but you can add the 1.4x TC to get 560mm at f6.3, and that combo should be right around 2kg.
I'm not sure that can recommend Fuji. The autofocus isn't up to par compared to other brand, and I don't find any of the lens options particularly compelling. Something like the X-H2S would be the right camera, but the 100-400mm lens is a bit old and not as good as other 100-400mm lenses. The Tamron 50-400mm isn't available for Fuji, sadly, although the 150-500mm is (heavier than your max though). The 150-600mm is big and heavy (although barely more than your 2kg + 10% limit), although it's actually lighter than the Tamron 150-500mm. Then there's the Fujinon 500mm f5.6. Great for birds and smaller animals, but since you're at 750mm (closer to 765mm) effective field of view, you're very limited without the zoom for other uses.
That leaves micro 4/3. The obvious choice is the OM Systems OM-1 Mk II. I'd pair that with the M.Zuiko Digital 100-400mm F5.0-6.3 IS II. You get 200-800mm effective field of view, and a teleconverter, while you can use one, is probably unnecessary (and possibly detrimental because you'd be introducing some diffraction). You already know about the advantages and disadvantages of the small M43 sensor.
I can't speak for anything in L mount. Never had any interest, so I haven't done the research. The one option I'm aware of would be the S1RII with the new 100-500mm. I've read the autofocus isn't up to par compared to Sony or Canon. Pretty much any Sigma lens is available in L mount, so there's that.
Out of all these options, I'd recommend going with the Canon 100-500mm lens and whatever body you prefer, even if you have to wait for it to be released. I hope I've helped you some, but if you're like me, knowing all the options makes things even more difficult.
