There can be living/anthro plants that aren't really connected to an "elemental" theme. It feels like a strange implication to me.

flora fauna are plant elementals.

In the 'earth, fire, air, water' thing some people interpret 'earth' as being plants.
Alternatively you could argue that all characters can be split among animals, mechanicals, and elementals.

But yeah, imo it doesn't really make much sense for all plant characters/creatures, particularly when you get into like, spec bio stuff or aliens.

Chinese philosophy has the wu-xing, commonly translated to English as the Chinese elements, although they aren't visualized as elemental substances as the Western ones are, but as interactions between opposites (to put it simply). They are Fire, Water, Earth, Metal, and Wood. As three of the wu-xing appear to match three Western elements, it's not hard to extend Paracelsus' notion of elemental beings towards Wood as well, as those beings are already associated with mythology and legend in the West (dryads, hamadryads, fauns, and other nature spirits).

Grass type irl