It might help for the folks here to know which brand and model of SSDs you have, what sort of sata controllers the sata ones are plugged into and what sort of cpu and motherboard the nvme one is connected to.
What I can say is Ubuntu 22.04 doesn't have some mystery problem with SSDs. I work in a place where we have in the order of 100 Ubuntu 22.04 installs running with SSDs, all either older intel ones or newer samsung ones. They go great.
If you haven't already, try running hdparm on your drive to get an idea of if the drives are at least doing large raw reads straight off the disk at an appropriate performance level.
This is output from the little NUC I'm using right now:
If your results are really poor for this test then it points more at the drive / cable / controller / linux controller driver.
If the results are okay, then the issue is probably something more like a logical partitioning / filesystem driver issue.
I'm not sure what a good benchmark application for Linux that tests the filesystem layer as well is other than bonnie++ which has been around forever. Someone else might have a more current idea of something to use for this.