At the very least this makes author's watch rather less unique and custom than described. Perhaps it was an one of a kind back in 2020, but it's not anymore.
OP’s watch appears to be a customized variant of the annual calendar LIGHT, which was introduced in 2016. The 36mm case is unusual, not one of the standard sizes, but O&J has been willing to do 36mm cases on request since ~2010 with certain models. So—like all O&J watches prior to 2020 or so¹—the cosmetics are fully customized, but the mechanism is shared with other O&J watches².
¹ since then they also have a collection of non-customizable watches
² this undersells it a bit; most O&J watches (like mine!) are "just" customized realizations of a set of basic designs (which is a good thing, IMO, because those designs work better than what most buyers would come up with). But many of those designs were developed collaboratively in response to specific customer requests. I was in the workshop in 2018 and saw an early prototype of what became the day/night watch (https://www.ochsundjunior.swiss/watches/day-night/) in development for the customer who had proposed it. If you skim through their blog, you'll find lots of interesting projects done for customers with varying degrees of customization (I really love this day/night done with no conventional face: https://www.ochsundjunior.swiss/dirks-day-night/)
It isn't super clear from first read, but that design is not by the author, but by the company. He gave them specs for what he wished for in a design, and they came up with a design.
At the very least this makes author's watch rather less unique and custom than described. Perhaps it was an one of a kind back in 2020, but it's not anymore.
The cost is around $9K.