There's this false competition between brands that we also see debated in forums.
Most invested in a brand will not switch. It's too expensive, too much hassle. And you lose the advantage of the experience you have acquired learning your current system.
This competition matters more to reviewers, who get to review all of the equipment from all brands, and so the competition narrative makes it more interesting for them and attracts more views/reads, etc, mostly from people who won't ever use the equipment and are kind of like spectators in a sports game.
But there is no Sony A9III and likely not to be for a while. Sony had to stop production on their popular A7SIII due to the chip shortage. I know one guy who would buy one if he could find one. They are still having problems meeting demand for their A1. Their next likely release is the A7 IV. They have no bandwidth for an a9III at this point and it wouldn't make much sense. Why compete against their higher priced A1, which they can't make enough of?
The a9III rumor was rated as a long shot even by SAR. So let's get rid of that notion.
If Canon says that the 1DXIII is still their flagship, then they almost have to price it lower than that model. Now how much lower we will see. But it won't make much sense for Canon to still proclaim that their 1DXIII is their flagship but have the R3 priced higher.