Your use case does not seem very computation-depending. Maybe a cheaper Raspberry Pi-based solution will also work.
Those models only have the "MacBook pro" "stick ssd" aka M2 SSD, which has a smaller form factor.
I have an Asus chromebox doing this, very happy with it.
That's the maximum capacity of a 2.5" 9mm tall drive. You can buy Seagate 4TB & 5TB drives in 2.5" which are 15mm tall. [0] [1]
[0] https://mtekk.us/archives/reviews/hardware/seagate-4tb-expan...
[1] https://www.amazon.com/Seagate-Barracuda-2-5-Inch-Internal-S...
I just did a build, and was considering the NUC, but it was prohibitively costlier for not a lot of improvement, other than the form factor.
You should be able to get a Thin Terminal device for about $100US with USB3.0 and gigabit ethernet and/or wifi. With a little shopping, you may even be able to get one with a low profile PCIe slot for similar money. A few examples of such machines are the HP T5740, t520 or t620. Dell/Wyse also should have acceptable options.
Choosing a Thin terminal should cost far less than a NUC while being much more capable than a raspberry pi for not much more money (a raspberry pi 3 still needs a uSD card, a case, and an unusually powerful USB PSU).
Its nice, though the performance of usb3 is... less than optimal the fact that I can saturate gigabit ethernet means I don't care too much. Local compiles are crazy fast though.
Its plenty fast for all my needs, though nfs over wifi is... slow in general its fast enough to not care a whole lot. I have a few bhyve linux vm's running that just go straight to the ssd's so they're silly fast with like 3g/s read speed or whatever. Its more than enough for all my home needs.
But many laptops will run without a battery just fine.