Tension roller timing belts axial play normal?

Hi, I have problems with noises from the engine compartment and strongly suspect that it comes from the timing belt drive I recently renewed. I have now installed the second timing belt set from Bosch, but still the same problem. Can anyone tell me if the axial game of the tensioning roll is so fine. I measure 2mm game. Here’s a video to illustrate:https://youtube.com/shorts/RqihmI6o4IM?si=SGFW-Z55fnS0Ml- And yes, in the vehicle, under tension, it had the same game. S o sounds like the whole thing then:https://youtube.com/shorts/fgpRGjicrrY?si=6iiOKZIewmZNGsXD The timing belt cover also has abrasion spots, so much so that the thing has been iced in the car. I already contacted Bosch and unfortunately got no statement whether 2mm is okay. I should contact the dealer. Well, you know how this ends. I’m very excited about your opinion. Thank you