I bought the Lexar NM710 when it was on a discount at the same time as I got the nvme base (basic), you can boot from it, it works nicely, but after a random amount of time (usually a few days), it’s like the Lexar goes into a sleep mode and can’t be waken up unless you reboot.
I switched it to a Samsung MZVPV512HDGL-000H1 (NVMe SSD Controller SM951/PM951) and it has been working flawless. In both cases used with dtparam=pciex1_gen=3
At the moment I’m not sure what to do with the Lexar, most likely it will just be a USB storage that njot ment to be connected for a long time.
Kingston KC3000 2TB SSD needs a quirk to prevent it from going to ps3/ps4 sleep modes, where it at least with current Home Assistant kernel (Linux homeassistant 6.12.47-haos-rasp) - crashes the system. Sounds the same as @trizt is reporting with Lexar.
You need to append this to end of boot/cmdline.txt nvme_core.default_ps_max_latency_us=0