Obsidian doesn’t (yet) support publishing to Wordpress; nor is there a plugin for that. There have been a couple of requests for Wordpress support, and I hope someone implements a plugin.
Until then, here’s a simple workaround: Obsidian is, among other things, a markdown editor, and other Markdown editors do support Wordpress publishing. So just compose in Obsidian, and use one of those other editors to publish. I’ve used IA Writer and it worked very nicely.
Why not just compose in the other Markdown editor, and skip Obsidian entirely? I prefer the way Obsidian handles embedded images, compared with other editors. Also, Obsidian is familiar. I don’t use IA Writer much anymore, so it’s not as familiar to me.
I haven’t tried this with multiple Obsidian documents simultaneously, just one at a time as individual posts to a Wordpress blog.