Would I actually notice SATA vs NVMe for games and Windows?

For everyday use and most games, the jump from a SATA SSD to NVMe is usually much less dramatic than the jump from a hard drive to any SSD. Windows and apps may open a little faster, and some games load faster, but huge benchmark numbers don't translate directly into huge time savings.

Loading depends on the game and the rest of the system too. A good SATA SSD is still perfectly usable if you already have one.

For a new build, compare actual prices and capacity. If a decent NVMe drive costs about the same as a SATA drive and your system supports it, NVMe is the easy pick. I wouldn't pay a big premium for a top-end PCIe 5.0 drive just for gaming, though. A PCIe 4.0 drive is plenty for that.

Don't expect an NVMe drive to boost your normal FPS. Storage mostly affects loading and asset streaming, not how quickly the graphics card renders a frame.

There are exceptions where storage can contribute to stutter, such as when a game is fetching assets or the system is short on RAM and using the page file. A faster drive may help in those cases, but it isn't a substitute for enough memory and won't fix every stutter.

SATA makes sense if your NVMe slots are full, your machine doesn't support NVMe, or you find a good SATA drive for less. For a game library, extra capacity can be more useful than chasing the fastest drive.

File-heavy work is a different question from launching apps. NVMe can be more useful when moving large files or running storage-intensive workloads, especially with multiple requests at once. Even then, the other drive and the task itself can limit the speed you see.