I put a tape measure up against the screen and measured roughly 200mm long by 40mm high, giving a length to height ratio of 200/40 = 5. If the SSD is 2280 form factor, 228/5 = 45.6, making the SSD approximately 46mm high, give or take a few mm.
To be on the safe side I'd say nearly 50mm or 2.0 inches high.
If your motherboard has an integral heatsink over the M.2 slot, you'll have to leave it off when you fit this beast.
If you're mounting it in an external enclosure (USB-C/Thunderbolt 4?), I'd allow a good 12mm (1/2") headroom, preferably more and you'll need good ventilation holes or a small fan. The more air flow, the better.
I've used this Inateck enclosure with integral fan on a normal 2280 M.2 drive with no heatsink of its own.
https://www.amazon.com/Inateck-Enclosure-Transmission-Supported-Applicable/dp/B097M8WQ6T