Just found the solution in the solution in the arch wiki. I needed to enable nscd for dns local cacheing, for some reason. After running sudo systemctl enable --now nscd, Steam now connects without an issue. I'm not sure why this just cropped up now, but I'm glad it's fixed.
Classic RTFM moment.
The Arch Wiki to the rescue yet again. 
Glad that fixed things, and thanks for reporting back.
If a recent change caused this behaviour, you might want to consider reporting this upstream.
Assuming you’ve got the necessary lib32- packages installed, this kind of sounds like an issue with your DNS resolver - if you have to refer to a local cache then the DNS resolver is not working correctly “after some time”. 
The section on the wiki talk page doesn’t shine much more light on why ncsd is needed…
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