I don't know it you saw, but Fujifilm just announced a version of the 500mm f/5.6 lens for their X-mount. Used with the X-T5, that will essentially give you 750mm with 40 megapixels (plenty of room to crop from there, if needed), at probably the lightest form factor for anything in the 750-800mm focal range (for prime lenses) currently available in any camera system. Given your experience with the Fujifilm system, I'd be curious to hear your opinion of whether that might work as a good walkaround kit for people who do a lot of songbird photography, but also a lot of hiking.
I think that even with the 1.4 teleconverter, the reach of the 200mm is not long enough for birding. You can use the 2X extender for more “reach” with a small decrease in image quality. I have used this lens for some sporting events & it has NOT disappointed me. The image quality is excellent . Shooting wide open helps to eliminate any distracting backgrounds & this lens is exceptionally built- almost “tank” like , durable components. Best wishes for your channel.
Looks like your 'birding' day out was much like mine tend to be 😎. A lot of my time's spent on local beaches, shooting surfing, so I invariably have the 100-400 + 1.4 t/c glued to the x-t4 (upgrade to x-t5 imminent 😉) & still don't get close enough! But hoping the 40mpx will help with cropping. The route home (I ride an Ebike) includes ~9 miles alongside the estuary of the river Camel, so waders, geese etc feature a lot - and huge distances 🥴. I see you have the gopro mounted on the hotshoe & I've just started to do the same, so it's a bit like looking down the barrel of a howitzer on my vids.
its not bad but if you're doing it professionally I'd suggest going full frame. Nikon or Sony imo. If you're just shooting for your kids then fuji is more than enough.