Does MusicXML support roman numerals and/or functions (such as T for tonic)? I know this can be done via a workaround, namely using lyrics and a special font. But I am talking about dedicated support.
Yes for roman numerals. Maybe for functions (such as T for tonic). Look into the element Harmony in direction.mod.
The harmony elements are based on Humdrum's **harm encoding, extended to support chord symbols in popular music as well as functional harmony analysis in classical music. ... The harmony object may be used for analysis or for chord symbols.
A root is a pitch name like C, D, E, where a function is an indication like I, II, III. Root is generally used with pop chord symbols, function with classical functional harmony. It is an either/or choice to avoid data inconsistency. Function requires that the key be specified in the encoding.