Mimicking `\chords` mode within `\markup`

[Joel C. Salomon]

\version "2.24.0"

\markup {
  Compare \sans\concat{F\char ##x266F °/C} to \sans\concat{F\sharp °/C}
  to \score{\chords{\chordmode{ fis:dim/c }}}
}

Looks like `\chords` is aligning the sharp symbol differently (and
probably using SMUFL U+E870 rather than U+B0 (°), but that matters
less).  How can I copy what `\chords` is doing?

(If the spacing and sizing of the embedded `\score` can be tweaked to
look like inline text, that's good too.)

I'm guessing that I need to somehow create a `ChordName` item, but I
can't see how to do so.

--Joel