The closest things to Bauhaus cameras that I'm aware of are the Nizo 8mm movie cameras such as the 801 (but it might be more accurate to call those "Ulm School")
As you said "the closest thing".
To my knowledge no Bauhaus lecturer or student ever designed a camera or similar. The designer of the Nizo 801 ("Braun design" as Braun by then had acquired Nizo) had no connection. The Braun chief designer, also doing photographic products, had no relation to Bauhaus either, but before worked together with the founder of the Ulm design academy.
Or think of Zapp, doing that iconic camera design. No Bauhaus connection either. Likely no formal higher education at all. Only decades later his design was brought to the mass market and became ubiquitous by Agfa who then presented it within a range of products resembling the "Braun Design" or Ulm school, though made by a designer with neither connection to Bauhaus or Ulm.
In its anniversary year this may sound blasphemic, but I think we must not over emphazise Bauhaus. It did not came out of the blue. But rather evolved out of a reform movement from the 19th century. A movement that showed new perspectives in spirituality, in man-nature relation, in body attitude (nudism, clothing), in design (Jugendstil, Arts&Crafts).
Concerning the design, there already was the concept of bringing together arts and crafts, in the so-called movement or in the german Werkkunstschulen. There even was such as the Gesamtkunstwerk were a artist/designer did a whole house up to the door knobs.
Also we must not overlook that there were even contradictory attitudes within Bauhaus. Best viualized in this still from a recent german tv movie depicting both Gropius and Itten:
Gropius in civil and Itten back then in a kind of habit. Itten approached the individuality of the student, Gropius wanted the student to be market orientated.
The Bauhaus also had to nourisch itself, by selling designs or products. And here the cash cow seems to have been.... textile. A product most people do not even have in mind at all when thinking of Bauhaus.
There also was back then that idea to establish Bauhaus as brand. A most successful project.
And that the Nazis rejected the Bauhaus (their strive to have control on each and everything already exuded an independant academy) does not exclude that some Bauhaus people accepted and even mingled with new regime.