Will my email client using SMIME have to implement this? Seems kind of ridiculous.

Seems to be targeting platforms. Will it be illegal to send encrypted texts, what is keeping anyone from using crypto on top of existing messaging?

While I do not want to dive into any details on adverse effects of such stupidities, the EU seems to be actually taking a strange road to tech dependent overengineered regulation. It seems that this mostly driven by lobbyists that want to sell compliance services. Also it seems that there is more value in creating regulation rather than making sure it is enforcible.