I've looked, what you say is mostly accurate but getting a bit dated - the NVME performance gap with SATA SSDs keeps widening especially with DirectStorage games (eg Spider Man 2 - triple the load speed vs SATA).
This gap will continue to widen as devs focus performance improvements on the tech available to them, and as the price difference between SATA SSDs and NVME is diminishing rapidly (only a 5% difference in common mid tier models now) there is very little reason to recommend SATA over NVMe for cost reasons - which was kinda the focus of this thread. I'd not advise anyone today to buy a SATA SSD over NVMe for gaming unless the cost saving was large.
First article I could find from a website I recognised (there are so many SEO-stuffing AI-generated trash sites today to wade through its truly frustrating) - https://www.techspot.com/article/3023-ssd-gaming-comparison-load-times/
The performance improvements outside of load times, eg during gaming are significant but harder to benchmark, because pop-in of assets during gameplay is not something we can currently easily measure, it's something you need to compare side by side videos of and there are many that show significant stuttering and pop-in for DirectStorage games like Ratchet and Clank. Another analysis with some videos double, triple or longer wait times in-games: https://www.youtube.com/watch?v=gl8wXT8F3W4