"Then, a mathbb{F}_{1^2} vectorspace V^{bullet} of dimension d is a set consisting of 2d elements V equipped with a free involution."

This can be considered a discrete, globally trivial covering space of degree 2 where GL is the group of deck transformations.

If rather than a free involution it was an involution with a single fixed point then it be a branched cover of degree 2 and a branch point at the fixed point of ramification index 1, a discrete counterpart of the Riemann surface for the square root. Orbit-stabilizer counting tells us that the number of points upstairs and downstairs have opposite parity. Topologically, this corresponds to the usual argument for relating the Euler characteristics of a branched cover and its base space, which proceeds by triangulating the ramification loci in the base space, extending that to a triangulation of the whole space, and then pulling it back to the total space of the branched cover. Then the covering map is simplicial and you can do orbit-stabilizer counting on the monodromy groups to compute the relationship between the Euler characteristics.

"For this reason, Kapranov and Smirnov invent the notion of an equivalence"

This is the same thing as a congruence relation in universal algebra for the algebraic theory of vector spaces of dimension n over F_q where q = 1 (mod n). Using the covering space analogy, it's an isomorphism of covering spaces, a map of total spaces that preserves fibers. From the categorical point of view, pointed covering spaces are diagrams of shape 1 -> W -> V and a morphism in this category between 1 -> W -> V and 1 -> W' -> V' is just a way of commutatively filling in the rungs with morphisms. Your statement that dim(X^{bullet}) equiv dim(Y^{bullet})~mod(n) then means that an isomorphism of covering spaces induces an isomorphism of base spaces.

If we were working with only locally trivial covering spaces, we'd have to substitute "locally" in a few places above. "Locally" is formalizable in terms of categorical localization. That notion becomes more interesting with branched covers, where localization should be equivalent to studying monodromy at different points. Going back to the Euler characteristic analogy I made before, the different non-free (nilpotency) points make additively independent contributions to the Euler characteristic, so there should be some sort of homomorphism from the product of all monodromy groups to the additive integers, giving the difference between the Euler characteristic upstairs and downstairs. The product of monodromy groups reminds me of adeles and the homomorphism into the integers reminds me of the total degree function on divisors.

That was a lot of random ideas. Assuming they are not nonsense, are these well known in the literature?

You said:

"In order to have a sensible notion of tensor-products we have to eliminate the n-factor."

You seem to have backed away from the guiding principle that vector spaces over F_un should be not mere sets but pointed sets. Then there is an analogy with pointed topological spaces, where the coproduct is wedge sum and the product is smash product. Now remember that the smash product can be constructed as the unpointed topological product divided by the wedge sum. When you decategorify spaces to dimensions then the quotient by the wedge sum becomes a division by the dimension of the wedge sum, what you call n.