Add a space after itemize only if no text follows

Question

I will start with an example of what I would like to do.

Here is some enumeration:
\begin{enumerate}
    \item First item.
    \item Second item.
\end{enumerate}
And the text continues in the same paragraph.
Here is some enumeration:
\begin{enumerate}
    \item First item.
    \item Second item.
\end{enumerate}
And the text continues, but in a new paragraph.

The code above should produce the following output (notice the spacing between the lines at the end of the itemize).

In some situations, I want to insert an enumeration (itemize or enumerate) inside a paragraph, and sometimes I want to insert it in the end and start a new paragraph after it, leaving an empty space. What I call a "paragraph" is not something starting with \paragraph{title} but simply a block of text delimited by empty lines in the code, which produces also a block of text delimited by two empty spaces in the output.

The mental image I have is that an enumeration is a part of my paragraph and I want it to behave the same way as anything else I put inside of my paragraph. So if it's the last thing in it, there should be a space after, and if not, then there should be no space. (Also, I put no space before my enumeration.)

I know how to always put a space after an enumeration or to never put anything after. But I don't know how to adapt the behaviour in the same way as when a paragraph ends. The way I do it now is to put no space by default and to add some \vspace{\parskip} if I end a paragraph with an enumeration.

How can I achieve what I described?

Complete example:

\documentclass{article}
\usepackage{parskip}
\usepackage{enumitem}
\setlist[1]{
  label=(\arabic*),
  % What do I do here to insert a space if there is a
  % new paragraph
  % after=\vspace{\parskip},
}
\begin{document}
\noindent
\section{Non-working example (no space)}
Here is some enumeration:
\begin{enumerate}
    \item First item.
    \item Second item.
\end{enumerate}
And the text continues in the same paragraph.
Here is some enumeration:
\begin{enumerate}
    \item First item.
    \item Second item.
\end{enumerate}
And the text continues, but in a new paragraph.
\section{Desired output (manual space)}
Here is some enumeration:
\begin{enumerate}
    \item First item.
    \item Second item.
\end{enumerate}
And the text continues in the same paragraph.
Here is some enumeration:
\begin{enumerate}
    \item First item.
    \item Second item.
\end{enumerate}
\vspace{\parskip}
And the text continues, but in a new paragraph.
\end{document}

Answer 1

Would this do?

\documentclass{article}
\usepackage{enumitem}
\setlength{\parskip}{10ex}
\setlength{\parindent}{0pt}
\newenvironment{enumerateD}{\begin{enumerate}[topsep=-\parskip]}
{\end{enumerate}\leavevmode\ignorespacesafterend}
\begin{document}
Test
\begin{enumerateD}
        \item Item
        \item Item 2
\end{enumerateD}
test\
test
Test
\begin{enumerateD}
        \item Item
        \item Item2
\end{enumerateD}
Test
\end{document}

Explanation

1. We are almost forced into loading enumitem, since we cannot easily change \topsep otherwise.
2. First we set \topsep to negative of the \parskip; by default the lists leave a vertical space of \topsep + \parskip (and also \partopsep if your list starts a new paragraph) at the beginning and end of the list. So we set \topsep to cancel out that defaul \parskip.
3. You don't want to use the \after code from enumitem, since this is executed before ending the list environment, which is too early. We want to throw something in right after ending the list environment.
4. Next, we want to detect a blank line that follows. What is useful here is that the list environment ends a paragraph with \par and ends up in vertical mode. Usually whether you put in a blank line has zero impact because \par is ignored in vertical mode. So what we will do is to force ourselves back in horizontal mode with \leavevmode. But once we are in horizontal mode, spaces are starting to be seen, so to avoid spurious spaces at the beginning of the line it is useful to also instruct \ignorespacesafterend.
5. The setting of \parskip to 10ex is just to make the effect more pronounced. Setting \parindent to 0pt is to mimic the desired output of shown by the OP where paragraphs are unindented.

---

mforbes asked in a comment for a solution when \parskip is not used. The following is one attempt at it.

It turns out that to test for characters automatically after the end of an environment is a bit difficult. This is because in latex.ltx you see that when you issue \end{envname} what happens at the end is

    ...
    \UseHook{env/envname/after}    %% This is when the \AfterEndEnvironment hooks are run
    \if@ignore\@ignorefalse\ignorespaces\fi  %% Mechanism for \ignorespacesafterend
}

Because of the \if@ignore...\fi it is not feasible to use any code in the After Environment Hook to detect subsequent \pars. This leads to our first observation:

To do what we want we have to modify the \end{envname} mechanism itself.

Next, I assume you would want \end{itemize}<space><newline><newline> and \end{itemize}<newline><newline> to behave the same. In other words, you would want to allow there to be spaces before the \par and still detect the \par; conversely, I also assume that in a situation where you don't want to ignore spaces, you wouldn't want this behavior either. So

Need to allow spaces to be gobbled. For this we refer to this previous answer. A side effect is that you have to issue \AtEndEnvironment{<envname>}{\ignorespacesafterend} to activate this mechanism.

More about the implementation:

• We define a new Boolean \@envendextrapar; the code detects (after gobbling spaces) whether the next token is \par. If so, it sets this boolean to be true, and otherwise do nothing.
• It is the user's responsibility to put code into \AfterEndEnvironment{<envname>}{...} using this boolean environment. For the example code below, if the \par is detected, an extra 2cm of space is added.

\documentclass{article}
\makeatletter
%%% From https://tex.stackexchange.com/a/432246/119
%%% A version of \futurelet that gobbles spaces
\def\futureletignorespaces#1#2{\def\nextaction{#2}%
  \def\checkspace{\ifx\nexttoken@sptoken
    \expandafter@firstoftwo
   \else
    \expandafter@secondoftwo
   \fi
   {\afterassignment\futureletagain\let\nexttoken= }
   {\futurelet#1\nextaction}}%
  \futurelet\nexttoken\checkspace}
\def\futureletagain{\futurelet\nexttoken\checkspace}
\newif\if@envendextrapar
@envendextraparfalse
\def\doEnvEnd#1{%
        \ifx@envendextrapartest\par\relax@envendextrapartrue\fi%
        \UseHook{env/#1/after}%
        @envendextraparfalse%
        \if@ignore@ignorefalse\ignorespaces\fi
}
@namedef{end }#1{%
  \romannumeral
    \IfHookEmptyTF{env/#1/end}%
        {\expandafter\z@}%
        {\z@\UseHook{env/#1/end}}%
    \csname end#1\endcsname@checkend{#1}%
    \expandafter\endgroup\if@endpe@doendpe\fi
    \if@ignore\def@tempa{\doEnvEnd{#1}}%
            \def@tempb{\futureletignorespaces@envendextrapartest@tempa}%
    \else\def@tempb{\UseHook{env/#1/after}}\fi%
    @tempb
}
\AtEndEnvironment{itemize}{\ignorespacesafterend}  %% Required, see explanation
\AfterEndEnvironment{itemize}{\if@envendextrapar \vspace{2cm}\fi}
\makeatother
\begin{document}
Test
\begin{itemize}
        \item First item
        \item Second item
\end{itemize}
Test again, no blank line.
Test start
\begin{itemize}
        \item Third item
        \item Fourth item
\end{itemize}
Test again, with blank line
\end{document}