It seems to me, more so than ever, that there is a continuum of jacket styles, perhaps not a straight line, but one with the occasional branch, (but still a range) from double breasted to single breasted and closed to single breasted and open fronted, and even to double breasted yet open fronted. Collars can be high, low, folded, or omitted entirely. So can lapels. Cuffs and tashes, buttons and buttonholes, all come and go. Some jackets can be worn more than one way- and we occasionally see pictures, especially on eBay, of jackets that are worn the wrong way.

Those in the business of selling jackets will have names for them. This helps to sell them. Those in the business of MAKING them may be less concerned about what a jacket-doublet-coatee-tunic is called and more about what the buyer wants it to look like and how it fits. And those who can have a jacket made need not worry about what to call it, other than their own.

I think we have established that someone can make this jacket and that others have similar ones, but also that its exact duplicate has not become common enough to merit a name. We have seen some interesting jackets and learned some interesting history along the way.

I hope the OP has the answer he was seeking.