I was confused when I started using https://github.com/pradyunsg/furo as I couldn't see the version-picker-links-to-builds-etc box when using that theme, to the point where I put in a feature request: https://github.com/pradyunsg/furo/issues/25
As @pradyunsg pointed out, I see it on the right now, but that's not where I'd expect it to be, and for some themes it ends up looking pretty ugly:
https://pip.pypa.io/en/stable/
The box to be in the left nav, roughly where it would be for the default theme
It's over on the right, where I don't expect it, and where it looks ugly on themes which have a left nav, which I would hazard a guess to be all of them.
I'm not sure _where_ we are adding this, but I think this should be configurable.
FWIW, Furo now does place this correctly in the sidebar, although it needed reading of sponsorship.js here, and a bunch more investigation.
Here is how stuff looks with the development documentation for pip (big file, screenshot):

The tracking issue for the mismatched colors is https://github.com/readthedocs/ethical-ad-client/issues/37
Oh, and here's what was the tracking issue for this on Furo's end: https://github.com/pradyunsg/furo/issues/23
Oh, unless we're talking about the hover box thingie -- in which case, WHOOPS, coz I was talking about the ads. :)
Yep, hover box thingy, which I think your screenshot still shows off on the right, whereas the RTD theme has it on the left, which I think it belongs...
@cjw296 Ah, I assume you mean the sidebar.
That's non-trivial for the embedding JS here (which applies to all of ReadTheDocs) to implement while still respecting any designs that themes could have (eg: only right sidebars like Sphinx's own documentation). I expect Furo to get the relevant styling for RTD settled down at some point, but that's not today. :)
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@cjw296 Ah, I assume you mean the sidebar.
That's non-trivial for the embedding JS here (which applies to all of ReadTheDocs) to implement while still respecting any designs that themes could have (eg: only right sidebars like Sphinx's own documentation). I expect Furo to get the relevant styling for RTD settled down at some point, but that's not today. :)