Just as an FYI - the previous version of the Sony RX10 is still available, and is $400-500 cheaper than the newest RX10 IV version. It has the same lens and essentially the same sensor - but just doesn't have the PDAF-based focusing system so it won't be as good with tracking moving subjects. For sharpness and clarity though, it will be among the best of any fixed lens cameras.
The FZ1000 also uses a 1" sensor like the Sony RX, so is also a good consideration - slightly less reach, but still much better IQ than the small-sensor superzooms.
And Canon also makes a 1" sensor superzoom, the G3X. Like the Sony RX10III, it won't be as good for tracking moving subjects, but has the same 600mm equivalent reach and larger sensor, so like the Sony and Fuji, image quality should be solid...and it sells in the $850 range.