Thank you @RoryMcPherson for the reply and tips. It's odd because I am admin AND owner of the dashboard I am trying to embed, as well as in groups it is shared to. I've tried it in multiple Teams I'm in. Also with different Dashboards and they don't work.
I tried adding layers and these work, but direct to browser, web maps (including the one in my Dashboard) work and display, Experience Builder and Instant Apps seem to show me with permissions but it just gets caught in a loading loop (I saw somewhere that they're not supported yet).
It's just the Dashboards that I don't seem to have permissions to view when I add them.