Redefine the abbreviated months with datetime2 package

Question

I was wondering if there is a way to redefine the abbreviated months with datetime2 package, such that, when using the command \today, months are written exactly like the first column of the image below.

\documentclass{article}
\usepackage[en-US]{datetime2}
\DTMlangsetup[en-US]{abbr}
\begin{document}
    \today
\end{document}

There is already a solution---How to make a lowercase month name with \today---with datetime package to redefine the month style, but this package creates a confit with my document.

Thanks.

EDIT in light of @quark67's solution:

I identified the conflict using quark67's solution to be with \usepackage[USenglish]{babel}, used for hyphenation. I just had to remove the argument [USenglish] to make quark67's solution works, but I would still like to keep \usepackage[USenglish]{babel}.

SOLUTION

In reference to this post: Redefinition of \today -- Clash with babel, placing @quark67's code inside \AtBeginDocument{...} solved it.

Answer 1

Try this (note the loading of the package datetime2-calc for the conversion from numeric value to the short month name).

Edit: As you say you need the document class ruthesis (https://scholarship.rice.edu/handle/1911/21747) in a comment, I update my code with this document class.

Also, as you have added a new requirement (June must be abbreviated as "June", no "Jun.", and July as "July", no "Jul."), I have updated the code (and corrected my dummy bug, May is never abbreviated as "May.")

Edit 2: "September" is abbreviated "Sept.", not "Sep.", as in the first column of the table.

\documentclass{ruthesis}
\usepackage[en-US]{datetime2}
\usepackage{datetime2-calc}

\DTMnewdatestyle{mydate}{%
   \renewcommand*{\DTMdisplaydate}[4]{%
   \edef\paramTwo{##2}%
   \def\monthV{05}%
   \def\monthVI{06}%
   \def\monthVII{07}%
   \def\monthIX{09}%
     \DTMshortmonthname{##2}%
     \ifx\paramTwo\monthV%
     \else\ifx\paramTwo\monthVI%
     e%
     \else\ifx\paramTwo\monthVII
     y%
     \else\ifx\paramTwo\monthIX
     t.%
     \else
     .%
     \fi\fi\fi\fi% 
     \ \DTMtwodigits{##3}, ##1}%
   \renewcommand*{\DTMDisplaydate}{\DTMdisplaydate}%
 }

\DTMsetdatestyle{mydate}

\begin{document}
    \today % Mar. 11, 2023
    
    \DTMdate{2023-06-11}
    
    \DTMdate{2023-05-11}
    
    \DTMdate{2023-04-11}
    
    \DTMdate{2023-07-11}
\end{document}

Result:

In a comment, you say that the previous code don't work because of a package you uses, but you don't say which additional packages you uses, so I cannot guarantee this code will work in your real usage.