Command \nr already defined (datetime2 and nccmath incompatibility)

Yes, they have a small incompatibility. The nccmath defines \nr to be equivalent to \\[0.5ex]. If you will not use this shortcut, then the solution proposed by @Zarko will work: nccmath will define \nr and datetime2 will overwrite it without problems.

But if you would like to have the \nr shortcut then that won't work. datetime2 uses \nr as a temporary macro to hold a number. You can redefine that to use another name, so the clash doesn't happen. Add this to your preamble after loading datetime2 and before nccmath:

\makeatletter
\define@choicekey{datetime2.sty}{useregional}[\DTM@val\DTM@nr]%
 {false,text,numeric,num}[text]%
 {%
   \ifcase\DTM@nr\relax
     \renewcommand*{\DTMifcaseregional}[3]{##1}%
   \or
     \renewcommand*{\DTMifcaseregional}[3]{##2}%
   \or
     \renewcommand*{\DTMifcaseregional}[3]{##3}%
   \or
     \renewcommand*{\DTMifcaseregional}[3]{##3}%
   \fi
 }
\let\nr\relax
\makeatother

MWE:

\documentclass{article}

\usepackage[useregional]{datetime2}
\makeatletter
\define@choicekey{datetime2.sty}{useregional}[\DTM@val\DTM@nr]%
 {false,text,numeric,num}[text]%
 {%
   \ifcase\DTM@nr\relax
     \renewcommand*{\DTMifcaseregional}[3]{##1}%
   \or
     \renewcommand*{\DTMifcaseregional}[3]{##2}%
   \or
     \renewcommand*{\DTMifcaseregional}[3]{##3}%
   \or
     \renewcommand*{\DTMifcaseregional}[3]{##3}%
   \fi
 }
\let\nr\relax
\makeatother
\usepackage{nccmath}
\usepackage{lipsum}

\title{Example}
\author{Isabella B.}

\begin{document}
    \maketitle

    \lipsum[1]

    \useshortskip

    \[ 2\times2=4 \]

    \lipsum[1]
\end{document}

You can load packages in this order, neutralising the \nr command from nccmath:

\usepackage{nccmath}%
\let\nr\relax%
\usepackage[useregional]{datetime2}

You can replace the nccmath \nr either with what it's for: \\[0.5ex], or use the linespread environment from mathtools (needless to load amsmath in this case).