In this situation, after halting and making sure that no train is approaching, do you have the right to proceed without waiting for permission from an authorised individual?

No. The visible B-32 sign says “Rogatka uszkodzona” (barrier damaged). You must stop before the sign unless another stopping point is designated. Under §26(2) of the Polish road signs and signals regulation, you may proceed only with permission from an authorised person or a signal permitting movement. Checking that no train is approaching is not enough.