Like all right thinking people, I abhor HTML emails but that’s a ship that sailed long ago and there’s not much choice other than grudging acceptance. The virtuous can, of course, continue to send plain text but sometimes your content or recipient really does need HTML. And truth be told, I often wish I could add some simple formatting like italics or bold.
David Wilson over at the System Crafters YouTube Channel has an excellent video on sending HTML with mu4e. The TL;DR is that you use org-mime to create a multipart email with plain text and HTML versions of your message. That’s pretty nice but the real win is using Org-mode to compose your emails. That lets you use the usual markup for things like bold and italics, add headers and links and all the other nice things that Org offers. Wilson’s video explains how to do all this and a couple of other things as well.
Sadly, this addresses only half the problem. The other side is rendering HTML messages that you receive. You’ve got eww but that often doesn’t work satisfactorily with emails. You can ask mu4e to display a message in your browser but then you’re leaving Emacs.
This is a good video and definitely worth watching. It runs 29 minutes, 12 seconds so you’ll have to schedule some time but if you’re a mu4e user you should definitely spend that time.