A Milliner.
A hat-maker is called a hatter, with the term milliner reserved for makers of women's hats.
a bag maker just like a hat maker i guess I do think you are right, no specific name, that I can find, for a maker of bags, however someone who makes hats is called a "milliner" if they make women's hats, a "hatter" if the make men's hats or more generally "Modiste" which can mean someone who makes hats and someone who makes garments.
A Hatter is someone who makes and sells hats (mens and womens) and a Milliner is someone who makes and sell womens hats
A milliner is a person who makes hats.
A baker is what you call someone who makes cakes. and Patisserie is the one who specialized in pastries and sweets.
Tapestrier.
A cutler
A Barista.
Legislator
Cartoonist
A baker.