Is only the top "veneer" profiled and then glued to a solid board below, or is the full thickness of the board profiled?
That type stuff is almost always made up as blanks in the form of planks, then run through automatic profilers. IOW, no way except for some of the custom matches we do, that the top layer would come separate.
in the second half of the 19th c. up until maybe the depression in the 20th c.; there was a common and widely installed product called "wood carpet". It's hay day was the decades just before WW1. it consisted of aproximately 5/16" thick feature elements arranged in geometric tiles and glued to linen backer. Contrary to the name ("wood carpet") it did not roll, but was delivered in more or less "large" sheets. It was laid out over diagonal T & G subfloor, and nailed down with "many" face nails/brads per element, in a geometric pattern.
Wood carpet border section, folded ribbon pattern, Office of the Treasurer, USA; 1860's
We replicate it for repairs or historic restorations with similar pieces to match, but glue them in. Sometimes we take up entire floors, catalog them, de-nail them, and then reinstall over diagonally laid
3/4" plywood (2 layers in gov't work) with modern adhesive.
I have posted in the past that with modern plywood and adhesives, this is a very practical and conservative method for modern complex floors. Think about it: 25/32" (standard thickness) T & G strip flooring is worn out when it had been sanded down about 3/16". The tops of the grooves start to split and feather off, and the 1/2" of wood under that is doing nothing if the flooring is laid over subfloor.
But as far as your post, all the "engineered" floors as in the PO's examples, are laid up complete in the factory. After cutting out, most with the micro-vee edge detail are also prefinished. (Some like Pergo and similar, the entire top layer is impregnated with dyed acrylic). The installers lay them out and glue them down.
Early 20th C "engineered floor" parquets, ballroom, Marjorie Post house (Hillwood Museum). Hide glue panel lay-ups, field installed in "cut back adhesive" (tar).
smt