Thank you for all your answers. I finally understood what was wrong.
First, I understood that a video IS not “16-235” or “0-255” in absolute but rather “optimized for a display in 16-235 (or 0-255)”.
So in premiere pro, I saw my video in a 0-255 space and it looked good. But I realized that my blacks were not always set to 0 so when the video was cropped to 16-235 on youtube, the blacks were too grey. The problem was solved by adjusting luminance and bringing the blacks to 0.
And I did not actually have a problem with “super whites” or “super blacks” since Premiere Pro cuts them off. So when the video was displayed in a 16-235 space, nothing when out of this range unlike in the video I posted in the first message.