\savebox within tikzpicture results in an empty \savebox

Question

Using \savebox within a tikzpicture environment seems wipe out the content of the \savebox. In the MWE below, the following macros define, measure and display the size of a \savebox:

\newcommand*{\DefineBoxAndItSize}{%
    \savebox\tempboxA{Hg}%
    %% https://tex.stackexchange.com/a/11945/4301
    \setlength\SizeOfBox{\dimexpr\ht\tempboxA+\dp\tempboxA\relax}%
}%
\newcommand*{\ShowBoxAndSize}{%
    Box \fbox{\usebox{\tempboxA}} is \printlength{\SizeOfBox}%
}

As long as \DefineBoxAndItSize is invoked outside of a tikzpicture, using \ShowBoxAndSize both outside (first line of output) and inside a tikzpicture environment (second line of output) works fine.

However, the third line invokes \DefineBoxAndItSize inside a tikzpicture before \ShowBoxAndSize, which ends up making the box empty.

Question:

How can I define a \savebox within a tikzpicture environment?

Code:

\documentclass[10pt]{article}
\usepackage{tikz}
\usepackage{printlen}
\newsavebox{\tempboxA}
\newlength{\SizeOfBox}
\fboxsep=0pt
\newcommand{\DefineBoxAndItSize}{%
    \savebox\tempboxA{Hg}%
    %% https://tex.stackexchange.com/a/11945/4301
    \setlength\SizeOfBox{\dimexpr\ht\tempboxA+\dp\tempboxA\relax}%
}%
\newcommand{\ShowBoxAndSize}{%
    Box \fbox{\usebox{\tempboxA}} is \printlength{\SizeOfBox}%
}
\begin{document}
    \DefineBoxAndItSize%
    \noindent
    Outside TikZ: \ShowBoxAndSize.
\medskip\noindent
\begin{tikzpicture}[inner sep=0pt, anchor=east]
    \node at (0,0) {Use inside TikZ: \ShowBoxAndSize.};
\end{tikzpicture}%

\medskip\noindent
\begin{tikzpicture}[inner sep=0pt, anchor=east]
    \DefineBoxAndItSize% <--- What is wrong with this?

    \node at (0,-1) {Define inside TikZ: \ShowBoxAndSize.};
\end{tikzpicture}%

\end{document}

Answer 1

Background: TikZ happens to gobble text unless it is an argument of a node. Even though this is sort of well known, this also has less obvious implications. In particular, saveboxes may end up being empty. This has already lead to confusion here and here. In the latter post, the OP solves the issue by wrapping their macro in \begin{pgfinterruptpicture} and \end{pgfinterruptpicture}.

The next step of sophistication, which may or may not deserve a new answer, might then be to wrap the savebox definition in an \begin{pgfinterruptpicture} and \end{pgfinterruptpicture} only if the macro is called inside a tikzpicture environment. To this end, the tests of this post and this post are employed. (Let me remark that the \IfInTikzPic is a bit unusual in that its first argument is the action that is to be taken if one is not in a tikzpicture environment. Whether or not this is related to the author driving on the other side of the road, I don't know. ;-)

\documentclass[10pt]{article}
\usepackage{tikz}
\usepackage{printlen}

\newsavebox{\tempboxA}
\newlength{\SizeOfBox}

\fboxsep=0pt

\makeatletter% from https://tex.stackexchange.com/a/458855/121799
\newcommand{\IfInTikzPic}{% https://tex.stackexchange.com/a/121309/4301
  \ifx\pgfpictureid\@undefined
    \expandafter\@firstoftwo
     \else
    \expandafter\@secondoftwo
    \fi
}
\makeatother


\newcommand*{\DefineBoxAndItSize}{%
\IfInTikzPic{\savebox\tempboxA{Hg}%
% https://tex.stackexchange.com/a/11945/4301
\setlength\SizeOfBox{\dimexpr\ht\tempboxA+\dp\tempboxA\relax}%
}{\begin{pgfinterruptpicture}%
\savebox\tempboxA{Hg}%
% https://tex.stackexchange.com/a/11945/4301
\setlength\SizeOfBox{\dimexpr\ht\tempboxA+\dp\tempboxA\relax}%
\end{pgfinterruptpicture}}
}%
\newcommand*{\ShowBoxAndSize}{%
    Box \fbox{\usebox{\tempboxA}} is \printlength{\SizeOfBox}%
}

\begin{document}
    \DefineBoxAndItSize%
    \noindent
    Outside TikZ: \ShowBoxAndSize.

    \medskip\noindent
    \begin{tikzpicture}[inner sep=0pt, anchor=east]
        \node at (0,0) {Use inside TikZ: \ShowBoxAndSize.};
    \end{tikzpicture}%

    \medskip\noindent
    \begin{tikzpicture}[inner sep=0pt, anchor=east]
        \DefineBoxAndItSize% <--- What is wrong with this?

        \node at (0,-1) {Define inside TikZ: \ShowBoxAndSize.};
    \end{tikzpicture}%
\end{document}

I'll be happy to remove this answer if people feel that this question is a duplicate and thus does not deserve a separate answer. (However, at the time of writing this, I am reputation capped, so the reason is certainly not to harvest reputation points, which it is in none of my posts.)

EDIT: Fixed a space, big thanks to Phelype Oleinik!