Short hair options with a hairpiece.
The hairpiece or wig has to have enough hair to hide the knots and base material. With growing hair, you could buzz down to a millimeter and all you would see is a tiny short hair coming out of the hair follicle on your scalp. But obviously a hairpiece is a base made of fabric or plastic that has hair tied to it, or looped through it etc.
So if you buzz a hairpiece down to much shorter than 2 cm, it can start to not look like your own hair, because it is not your own hair. You will start to see things that should not be seen, such as lace, knots, wrinkles, ripples, adhesive products etc.
However there is a way to wear a hairpiece as opposed to a full wig without having long hair at your back and sides. That is of course the “disconnected undercut”. This is a hairstyle that people who do not suffer from hair loss are increasingly choosing. The hair at the front, top and crown is very long, and the hair at the back and sides is cropped really short. You can do this with a hairpiece, as long as you have reasonable density in your remaining real hair.
Search online for photos and video of the disconnected undercut to see how this is easily applied to a hairpiece if your real hair is extremely short.