Stephen's plugin above (WP-Markdown) is brilliant for simple posts where conversion to HTML and back will do no harm. Sadly footnotes don't convert both ways very well (if at all).
After much research (and years of use of Markdown on Save Improved), I've switched to Robin Adrianse's Parsedown for WordPress. It makes Markdown available everywhere for both posts and comments. It's a bit tricky for very complex posts as all posts are parsed as Markdown first (HTML is still parsed as HTML is part of Markdown spec) but for comments it works with no issues at all. Either Markdown or HTML comments are supported, transparently. Nothing is permanently converted. Whatever you type in is converted to HTML on display. When you reopen a post, you get the original Markdown.
I recommend switching to plain text editor to avoid any cross-conversion/parsing issues with the TinyMCE editor or more specifically WordPress's own reparsing of text (WP autop filter). There are no performance issues I can see if one is using a caching plugin (who the heck isn't in 2021).
I specify Robin Adrianse's version of Parsedown as there are several other versions which go too far, converting HTML to Markdown permanently. Parsedown for WordPress works fine with WordPress 5.8 and Classic Editor so ignore any version warnings. Robin Adrianse no longer uses WordPress so cannot be bothered keeping up with the never-ending version number changing (real hassle for developers who are mostly volunteers providing open source code).