Are you obliged in this situation to make sure that there is no tram approaching?

In the video you pass sign A-21 "tram" and approach a junction with traffic lights, where you cross tram tracks; you have a green light. Even so, you are obliged to make sure that no tram is coming. The answer is: yes.

The Road Traffic Act requires you, before entering the tracks, to make sure that no rail vehicle is approaching, and it applies this rule accordingly when crossing tram tracks; sign A-21 warns of such a place. A green light gives you right of way, but a tram weighs several dozen tonnes, needs tens of metres to brake, and the tram driver can also make a mistake. A look left and right before the tracks takes one second, and it protects you from the most dangerous type of collision in town.

Legal basis: Art. 28 para. 1 and 6 of the Road Traffic Act (Prawo o ruchu drogowym); § 10 para. 3 of the Regulation on road signs and signals