While I agree with others pointing out the oddity of a portable server in general: this sounds like a great use-case for a laptop.
Built-in battery, wifi you can broadcast out as a hotspot, and it even has a display/keyboard/mouse for troubleshooting!
An older laptop with the optical drive stripped out could have a 2.5” 5TB HDD in addition to the boot drive for some decent mobile storage.
What’s rough about it? I’ve never been a twitter guy so can’t really compare, but I have a Mastodon account that I pop into periodically, and it works fine.