This was recently kinda misrepresented in the media, in my opinion.
Yes, notifications can leave traces. But it’s traces on the device itself that can be forensically extracted. Though notifications are pushed through Apple’s/Google’s servers, the contents are encrypted end-to-end.
Well DMCA doesn’t apply outside of the US. Lawyers continually try to enforce it abroad, though, so be sure you pick a web host that adheres to Norwegian law only.