I know this is a joke, but... NetBSD has a Dreamcast port so it's definitely not out of the realm of possibility that you could make a Hexbear post on a Dreamcast using a terminal-based web browser or some bare bones HTTP client if you have one of those expansion cards that lets you connect to the internet.
Damn I wonder what compatibility is like for that browser.
I know this is a joke, but... NetBSD has a Dreamcast port so it's definitely not out of the realm of possibility that you could make a Hexbear post on a Dreamcast using a terminal-based web browser or some bare bones HTTP client if you have one of those expansion cards that lets you connect to the internet.
X.org server on NetBSD/dreamcast 9.1
I found a YouTube link in your comment. Here are links to the same video on alternative frontends that protect your privacy: