Align text based on decimal marker

[josephwright]

As discussed in Aligning text in S columns in a way that respects the decimal marker for numerical entries, provide an alignment option to centre text relative to the decimal marker. May also be worth looking at an 'offset'.

[sim642]

In addition to centering text with the decimal marker, I'm interested in something similar to https://tex.stackexchange.com/questions/599661/siunitx-aligning-infty-in-an-s-column because input-digits=0123456789\ding{51} doesn't work (every cell gets some 11 prepended for reasons I don't understand).

So as to offset possibilities, something like "left-of-decimal" and "right-of-decimal" (or however to call them) would be nice.