That HDMI power has some grunt behind it. During power-off state with that 1.90v phantom voltage, I put a 48ohm resistor between 3V3 and ground, the phantom voltage only dropped to 1.80v, and the SSD still didn't work when I powered the machine back on.
Try more resistors in series? (or just a bigger one if you have any -- scratch that we needed smaller ;-) ).
Well... Needed smaller in terms of resistance, but needed bigger in terms of power rating, in the interests of not catching fire.
Does it sound like reverse current through SBD? They have higher reverse current and leaky I-V curve. 3.3V of drop must mean something inline.
The amount of leakage is on the high side, so it does point to some device that is wired to the standby power that is probably 'powering' the 3.3v line via some ESD network between the power rail and pads. this is usually indicative of a part that was not chosen correctly for the job, or the correct part was wired to the wrong power bus.
If I were the designer I'd put the resistor in, power down the system, get a cup of coffee, come back and image the system with a thermal imager and the problem chip will be the 'hot one' (slightly warm, if you're unlucky its hot enough to just feel with your finger).
2 watts static current is nothing for a beefy PC motherboard but it will need a special heat sunk resistor which is annoying. The bigger problem is whatever is supplying the leakage is possibly an i/o pad and eventually that thing will fry if you keep pulling power from it (but from the description this feels possibly like a buck regulator that is 'off' and just leaking current, in which case it's fine to draw that amount of power).
It's one of those annoying things where it's hard to say who did what wrong. On the one hand, you could say the motherboard is out of spec by not bringing 3.3v to 0; but in reality 'we all know' that at power off things always hang out around 0.7v (a diode drop above ground) for a very long time without active countermeasures. on the other hand you can say the drive is out of spec for not going into reset when 3.3v goes out of regulation. I haven't looked at the atx spec specifically so maybe this edge case is specified, but when you are doing a fully integrated design this is just one of the things you learn to check for in integration testing.
A dirty fix could be to just put a static load on the 3.3v line to ground. I'd start with a 1/4w resistor around 100 ohms and just stick it from 3.3v to ground to see if that does not soak up the stray current. if it works just leave it, it's about 0.1 watts of static power and no big deal for a non portable setup.
The larger picture is that the controller on the nvme might not hit its power on reset condition because it may be rated to run at 1.8v (just a guess), so 3.3v is not going low enough for the controller to perceive the system has been power cycled. Usually a supplemental power monitor is needed in those cases to ensure a reset is generated in case of leakage problems like this.