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I wouldn't dare actually review CSS, but I looked at the screenshots, and in the light theme it seems you actually darkened the bg color for inline code. Have you tried just leaving that bg color out (so it's presumably the same as for regular text)? What made you darken it? As a compromise I would be happy if the color scheme used was the same as in the latest (dev) Python docs -- except I can't seem to find much uniformity in that: when a code word is a link it has no darker bg, when it isn't, I've found examples where code has a darker bg and examples where it doesn't, sometimes on the same page, so that's still a mystery.

in the light theme it seems you actually darkened the bg color for inline code

Yes, slightly, from #f8f8f8 to #eeeee, which is a consistent shade with the CPython docs at #ecf0f3 for code literals and the rest of the PEP theme palette.

Have you tried just leaving that bg color out (so it's presumably the same as for regular text)?

Yes, but its much harder to tell apart from regular text (and looks as much like medium-bold text as anything), more difficult to tell exactly where the literal begins and ends, and not consistent with the CPython docs and the great majority of Sphinx themes (the built-in ones, Lutra, Furo, etc).

What made you darken it?

This was initially to, as we discussed on Discord, ensure it was at least darker than the zebra striping (with an additional offset applied depending on whether it was on a colored stripe, to maintain relative contrast). However, I retained it in the final version, as it ensured the background color is actually properly visible to most people on most monitors (as it was nearly invisible before, at least in light mode, while it was very visible in dark mode, which I made less so), is consistent with the CPython docs, and helps convey the semantic difference between code literals and object references.

As a compromise I would be happy if the color scheme used was the same as in the latest (dev) Python docs

It is now essentially the same shade as the CPython docs theme, slightly simplified to follow the standardized and a11y contrast-tweaked PEP theme color palette.

except I can't seem to find much uniformity in that: when a code word is a link it has no darker bg, when it isn't, I've found examples where code has a darker bg and examples where it doesn't, sometimes on the same page, so that's still a mystery.

This is because they are using different markup that have different semantic meaning (just like the other things you're used to seeing :). References to defined names/objects, like functions, classes, methods and modules, have no background (e.g. :func:`print`, :mod:`sys`, :class:`sqlite3.Connection, etc), while regular literals (Path("some/path/to"file"), r"\b(\w)+\b", OSError: The file could not be found, etc) do. However, these constructs have not always been used consistently in Python's documentation, so it isn't always obvious at first glance unless looking at the source.