What replaces the "Edit Message" button in the New Outlook?

Now try it in "New outlook" :)

That is how you do it in old outlook. The option is not there for new outlook.

Open your message so it opens the email in its own window. Expanding it to full screen is helpful so you can find the next steps easier.

Click MESSAGE.
Go to the section that says Move.

Click the drop down arrow next to "Actions"

You'll find EDIT MESSAGE there.

Those instructions apply to "Classic" Outlook, not "New" Outlook. And in "Classic" Outlook you have the further option to add "Edit Message" (with icon) to the ribbon, so that you don't need to do all those steps each time. Nothing about editing a received message has changed in "Classic" Outlook, and the feature is not yet provided in "New" Outlook, so the problem remains.

There are articles available at various sites like Office Watch explaining some of the underlying major differences between the classic and new Outlook programs. They are very different "under the hood". The true replacement for "Classic" Outlook may still be more than a year away. I wonder whether Microsoft is keeping their fingers crossed they can just abandon that project. "Classic" Outlook is very old software that would need a thorough overhaul to fix its quirks and problems. But there are users like me who won't switch to "New" Outlook in its current state of development.