You say you wanted to do a 2D analysis, but you are doing a 3D analysis and holding some DOF at zero to keep the nodes constrained to a plane. There is an actual 2D setting for analysis that you could use instead of doing a 3D analysis and holding nodes at zero in some DOF.
I understand that you want to simulate the model in the XY plane and that the beam is along the Y axis. Therefore, you want to set the Z translation to zero and you also want the rotations about X and Y to be zero. That is a symmetry BC to create a planar result. The free DOF are therefore X and Y translations and Z rotations. Why did you set Y to be zero? I think that is a mistake.
I repeat my point that buckling generally requires a tiny perturbation in the geometry to seed the solution with the buckled shape. To have a successful nonlinear buckling solution requires that you turn on Large Deflection and I suggest that you turn on Auto Time Stepping and set the Initial and Minimum Substeps to 100 and set the Maximum Substeps to 1000.