centralising markups above notes

[Gilberto Agostinho]

Hi everyone,

I'm trying to add centred string numbers to some notes in my composition 
using markup. Using only \center-align as the documentation suggests 
does not seem to do the trick, as the text is still not centralised. I 
am only able to get them properly centred when I set parent-alignment-X 
to zero AND use \center-align. Am I doing something incorrect or do I 
really need these two commands in order to get the text centred?

Minimal example: 4 bars, only last one seems to be properly centered

\version "2.23.0"
{
    % regular markup: left aligned
    d''1
    ^ \markup { III. }

    % \center-aligned: still not centered
    d''1
    ^ \markup { \center-align III. }

    % setting parent-alignment-X to 0: still not centered
    \once \override TextScript.parent-alignment-X = #0
    d''1
    ^ \markup { III. }

    % setting parent-alignment-X to 0 with \center-aligned: now it's 
properly centered
    \once \override TextScript.parent-alignment-X = #0
    d''1
    ^ \markup { \center-align III. }
}

Producing: 
https://i.postimg.cc/ZKVTyn6L/Screenshot-from-2021-04-09-11-30-58.png

Many thanks,
Gilberto