We're looking for vertical to horizontal switching. Not just examples of vertical writing.
Almost all extant vertically-written languages are more commonly seen horizontally on the web. Vertical Japanese on the web (from my American understanding) is a design choice, and is notably absent from mainstays like https://www.yahoo.co.jp/
That is to say, it is unlikely that a site's language switcher would opt for top-to-bottom writing.
Edit: the Mongolian president's site does have an English version! ...but it's a completely different site :( https://president.mn/en/. Still, this is the closest to a use case for logical properties I've seen, so kudos.
It's unlikely (I'd guess) that a site would want to offer the exact same page in both horizontal and vertical modes, yes. But it's plausible they might want to share a lot of design elements between horizontal and vertical versions of the content.
Using logical properties would make it easier to have a common base of CSS that controls spacing, sizes, etc., that can be used by both language versions, rather than maintaining them completely separately.
> the arguments for these properties revolve around, "well, what if I decide to use traditional Mongolian in the future?," which seems like the biggest case of YAGNI I can think of
...And even this one close example doesn't use them!
Other examples (e.g. vertical Japanese) aren't too hard to find: https://nishinokensetsukogyo.co.jp https://ok-maru.jp etc.