Browsing Eukaryota's wikipedia article is an adventure

I think they are classified in the plant kingdom by most if not all, I was being sloppy with my terms. They are very different from what we think of as plants typically though, seaweed is a colony of single celled organisms more than "a plant"

Seaweed

Seaweed is a type of macroalgae. It's debatable if algae count as plants or not, they are photosynthetic but are in many ways their own weird form of single celled organism