How to draw a PGF picture in front of any other PGF picture?

Question

I saved the following LaTeX code in the file ~\Test.tex.

\documentclass{beamer}
\usepackage{tikz}
\usetheme{Warsaw}
\begin{document}
\begin{frame}{Frame Title}
    \begin{tikzpicture}
       \draw[fill,red](0,0)rectangle(\textwidth,\textheight);
       \draw[fill,orange](0,0)circle(2pt);
       \draw[fill,orange](\textwidth,\textheight)circle(2pt);
    \end{tikzpicture}
\end{frame}
\end{document}

The code creates a beamer presentation whose theme is Warsaw. (The Warsaw theme adds headers and footers to every frame.) The presentation consists of a single, regular frame. The frame's content consists of a single object: a TikZ picture. The picture is composed of three elements: a filled red rectangle whose width is \textwidth and whose height is \textheight, and two filled orange circles at the bottom left and top right corners of the red rectangle.

I then executed the following commands in the Terminal.

> cd ~
> lualatex Test
> lualatex Test

At the end of the compilation ~/Test.log did not contain any instructions to rerun the compilation. The compilation resulted in the creation of the file ~/Test.pdf. When opened in a PDF viewer, the file displayed as follows.

As can be seen, the orange circle at the top right corner of the red rectangle is visible, but the one at the bottom left corner is invisible. This indicates that part of the red rectangle is hidden behind the black and blue footer.

---

Questions

1. How can the red rectangle be drawn in front of the footer?
2. More generally, how can a TikZ picture be drawn in front of any other TikZ picture that overlaps it, even without knowing which TikZ pictures, if any, actually overlap it, or even if there are any other TikZ pictures in the document?
3. Even more generally, how can a PGF picture be drawn in front of any other PGF picture? (Apparently the footer of a beamer presentation of the Warsaw theme is not a TikZ picture, but a PGF picture. Moreover, every TikZ picture is a PGF picture, but not vice versa.)

Answer 1

If you want to print some thing on top off everything you have to add it after the footer. You can e.g. use the shipout/foreground hook. When calculating the sizes, be aware that \textheight in beamer is much larger than you expect. It actually goes down to the bottom of the frame.

\documentclass{beamer}
\usepackage{tikz}
\usetheme{Warsaw}
\begin{document}
\makeatletter
\AddToHook{shipout/foreground}{%
  \put(1cm,-\paperheight){%
       \begin{tikzpicture}
       \draw[fill,red,use as bounding box](0,0)rectangle(\textwidth,\paperheight);
       \draw[fill,orange](0,0)circle(2pt);
       \draw[fill,orange](\textwidth,\paperheight)circle(2pt);
       \draw[<->,green,line width=3pt](-2pt,0)--++(0,\textheight);
       \end{tikzpicture}}
       }
\begin{frame}[t]{Frame Title}
\mbox{}
\end{frame}
\end{document}

Answer 2

I'd like to suggest a variation on Ulrike Fischer's answer. The variation avoids the \put command, and instead positions the elements of the TikZ picture relative to the current page pseudo-node.

\documentclass{beamer}
\usepackage{tikz}
\usetikzlibrary{calc,math}
\usetheme{Warsaw}
\begin{document}
\AddToHook{shipout/foreground}{%
   \begin{tikzpicture}[remember picture, overlay]
      \tikzmath{
         coordinate \origin;
         \origin = (current page.south west) + (1,0);
      }
      \draw[fill,red](\origin)rectangle++(\textwidth,\paperheight);
      \draw[fill,orange](\origin)circle(2pt);
      \draw[fill,orange]($(\origin)+(\textwidth,\paperheight)$)circle(2pt);
      \draw[<->,green,line width=3pt]($(\origin)+(-2pt,0)$)--++(0,\textheight);
   \end{tikzpicture}%
}
\begin{frame}{Frame Title}
\end{frame}
\end{document}

The output in both cases is the same:

Answer 3

If you look at Figure 1 of the beamer user guide, you'll see that the footline is drawn as the very top layer of a beamer frame. If you don't want it from covering your frame content, you can use a layer further down to show the footline.

\documentclass{beamer}
\usetheme{Warsaw}
\usepackage{tikz}
\setbeamertemplate{footline}{\vskip3.625ex}
\makeatletter
\setbeamertemplate{sidebar canvas left}
  {%
  \tiny%
  \leavevmode%
  \hbox{%
  \rule{0pt}{\dimexpr\paperheight-1.125ex}%
  \hbox{\begin{beamercolorbox}[wd=.5\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm plus1fill,rightskip=.3cm]{author in head/foot}%
    \usebeamerfont{author in head/foot}\insertshortauthor
  \end{beamercolorbox}%
  \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.5ex,dp=1.125ex,leftskip=.3cm,rightskip=.3cm plus1fil]{title in head/foot}%
    \usebeamerfont{title in head/foot}\insertshorttitle\nobreak\hfill\usebeamercolor[fg]{page number in head/foot}\usebeamerfont{page number in head/foot}\usebeamertemplate{page number in head/foot}
  \end{beamercolorbox}}}%
  \vskip0pt%
  }
\makeatother
\begin{document}
\begin{frame}{Frame Title}
    \begin{tikzpicture}
       \drawfill,redrectangle(\textwidth,\textheight);
       \drawfill,orangecircle(2pt);
       \drawfill,orangecircle(2pt);
    \end{tikzpicture}
\end{frame}
\end{document}