I suggest simply using outset
for the y-axis, this will leave the baseline unaffected:
#let part(content, angle: 0deg, content_color: black) = {
box(
radius: 0.1em,
stroke: (2pt + oklch(40%, 0.2, angle, 100%)),
fill: oklch(95%, 0.05, angle, 80%),
inset: (x: 0.3em),
outset: (y: 0.3em),
)[#text(content_color)[#content]]
}
x-inset + y-outset is the go-to style for inline raw in most of my documents and it served me pretty well.
I think this also has the added benefit of not affecting line spacing, in case the baseline option does, I’m not 100% sure about that. But this also means for tight line spacing this will intersect with the other lines.