A person who sews is called a seamstress (not sure what the male or un-gendered version of that is), a person who makes embroideries is called an embroiderer, a person who does calligraphy is called a calligrapher, ... what is a person who weaves tapestries called? The obvious answer is a weaver, but that is someone who works at a loom and tapestry makers do not work that way.
"Weaver" implies someone who weaves, and to weave is to "form (fabric or a fabric item) by interlacing long threads passing in one direction with others at a right angle to them." That is not what a person making a tapestry does.
If the single word differs between hobbyists and professionals I would be interested in either.