SCART to HDMI adapter restrictions?

I wanted to get my old Playstation 2 or the very first Xbox out again.
However, my TV has only HDMI ports and no SCART connection.

I've already asked ma employee in a media market if there are adapters for it. He meant so but you can't do everything without restrictions.

Is that correct? Or can I use it without problems the old consoles? That it is no longer HD is clear to me.

Yes, sometimes you have strong quality losses, the picture has color errors and partly trembling stripes.

My adapter is now in electronic waste - unfortunately had no such good adviser in the media market.