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.
The “tapestry kits” are actually needlepoint and not tapestry. From Wikipedia:
Needlepoint is often referred to as “tapestry” in the United Kingdom and sometimes as “canvas work”.
One stitches needlepoint.
What would you call somebody who does needlepoint? You call them a needlepointer. (Variously spelled as one word, two words, or hyphenated.)
But suppose you are mistakenly calling needlepoint tapestry? You probably don’t want to use the word needlepointer. The word needlework covers a number of textile arts, so you can call somebody who makes needlepoint “tapestries” a needleworker.