That said, I think I may recently have found the cheapest possible travel guitar solution. I bought one of these and I keep it in my locker at work, to play in the occasional lunchbreak:
https://www.thomann.de/gb/startone_cg_851_12.htm

It's a 1/2 size classical guitar. It cost me £30 (£40 including delivery).

Rather amazingly for a £30 instrument, the intonation is spot on and it's actually a fun instrument to play, with a decent tone to it. It has a nut width of 45mm, so actually still slightly wider than a conventional full-size steel string guitar, which is normally 43mm. (Though the advertised 45mm feels to me more like 43mm in practice when I'm playing it)

They do the same basic Startone classical guitar in 3/4 size and 1/4 sizes (and indeed full size) for the same price or even less, depending on whether your idea of a travel guitar can afford to be a bit longer, or needs to be even smaller.