Macro Econ 101 says you're wrong. Increasing supply is increasing supply. Raising prices of luxury (non-essential) goods always reduces marginal demand.
It is theoretically possible that Sony and MS can't pay their way to more console components. But, as a lifelong business person, I know that's not true in practice. There is capacity to meet some customer orders, just not all of them, so it is an absolute certainty that money is influencing who gets the stuff that can be supplied.
That are two points in your post:
1) Gaming hardware aren't really luxury products in the right definition of the word. Luxury products are the ones which price increase don't actually decrease demand (or at least not decrease as fast), that's because of the status that said product brings is deeply rooted in the perceived value of the brand, that's the case of fancy cars like BMW and luxury clothes brand. Which decrease demand for luxury products is generally the decrease of the income, seeing how much consoles sales increased when we had crisis and people losing their jobs due to Covid is safe to sell consoles are no longer luxury products. Of course, the definition of a luxury product will vary from region to region, but it's hard to believe consoles with a potential 300 million market can still be labeled as luxury
2) Oligopolies don't work in the same way as traditional markets: https://www.economicsonline.co.uk/Business_economics/Oligopoly.html
"The theory of oligopoly suggests that, once a price has been determined, will stick it at this price. This is largely because firms cannot pursue independent strategies. For example, if an airline raises the price of its tickets from London to New York, rivals will not follow suit and the airline will lose revenue – the demand curve for the price increase is relatively elastic. Rivals have no need to follow suit because it is to their competitive advantage to keep their prices as they are.
However, if the airline lowers its price, rivals would be forced to follow suit and drop their prices in response. Again, the airline will lose sales revenue and market share. The demand curve is relatively inelastic in this context."
I don't know exactly what was your business, but I suppose you understand not every business is the same. Every market will behave differently. If you want to see price elasticity in work for consoles I guess we can come back to PS3 and Xbone launch prices, the high launch price lead them to decrease in sales (short therm)
If their point is to reduce shortages making people stop buying, then you got a point. Increasing price will lead to reduce in hardware demand but... what's the point.. really? I don't see why a company would choose to lower their demand purposefully. The only way for either MS and Sony really increase their prices would be a veiled agreement to both, and then this would only cause an increase in demand for other consoles (Switch) or even PCs, both companies would only lose market share