Thank you for putting my thoughts into much more eloquent words!

Before they attach to a rock they move around in a larval stage, same for anemones and some jellyfish species. There are exceptions to all of our classifications because nature doesn’t have to play by any rules besides physics. Even the concept of species has no set definition because no matter what we come up with there are exceptions. Also “seek out” was a bit too specific, they have to take in food from outside themselves as they can’t make their own energy like plants.

No trees are plants and fungi are fungi. Animals are multicellular organisms that are mobile and seek out food at a very basic description. Plants are multicellular non mobile that make their own food and fungi are somewhere between that. Closer to animals but not. Then there’s the single cell life of bacteria and archea.