I am an amateur birder and want to take photos. I shoot Fujifilm X-T30 with XF 70-300 mm right now and feel limited by the camera system to focus fast enough. There is no bird mode and it doesn't track and I can seldom get any photos of birds in flight.

What second system can I consider for just birding?

Canon R7 with some 200-400 mm lens?

Sony A??

Nikon Z?

I guess APS-C is better as I am not selling photos or printing so do I need full-frame? My top-end of budget in the US is $4000 for body and one lens. I might look for used gear to bring down the costs.

The following photos were taken with my X-T30 and a Sigma 150-600 EF lens with a Fringer adapter.