Ah, apologies I missed that bit.
Sony have not clarified the process by which the PS5 qualifies a NVMe drive for use but I expect it be to an I/O stress test. So the first two scenarios/drives eastmen mentioned would fail this test and couldn't be used.
A cheap/fast drive might work, the only question is the thermals. I'd argue this is the drive's problem but if Sony put a thermal sensor in the enclosure to prevent stupidly hot drives, that could be a factor for rejecting it as suitable. I would be surprised though, although some drives have heatsinks and/or fans, they're not running at CPU/GPU temps.
But to be clear, we know - because Sony have said - PS5 will only support drives that are as fast managing the various priorities of traffic as the internal drive and because NVMe has fewer priority levels, the drive I/O actually needs to be faster overall than the internal drive.