If we consider the pins on the top and bottom brackets free to rotate the system will buckle randomly either way, to right or left. With the first buckling column changing the geometry of the system and sparing the other one from buckling.
Unless the width, $\theta \geq L/10$, or whatever short column index for this material, the $K=1$.
However, The effective force will be $1/2P$ at the start of bifurcation of the column buckling.
After OP's comment.
Long slender columns behave even more clearly the way I explained; as we increase load P the columns are sharing equally half of the load, then at exactly the point where P, reaches the critical buckling load, randomly and explosively one of the columns fails and becomes the pathway for the force P. And due to the freedom of the pin connection the top or bottom header or both rotate and the system becomes a mechanism, collapsing in a nonrecoverable buckle.
It is notable that even for a system of 3 or more columns the collapse always starts from an end column and then sometimes progresses to the next one down the line. I have observed similar situations in damage to the soft-story buildings in the Northridge earthquake of 1994 when I was preparing Seismic damage estimate reports for the owners of the buildings.