All PDF manipulations - nice and open src (pypdf would be an alternative - see below)

combine.tex

\documentclass{article}
\usepackage{pdfpages}
\usepackage{background}
\backgroundsetup{scale = 1, angle = 0, opacity = 1,
   contents = {\includegraphics[width = \paperwidth,
   height = \paperheight, keepaspectratio]
   {testbriefkopf.pdf}}}
% for different, we can have two steps: first background, then merge
\begin{document}
\includepdf[pages=-]{dinbrief2.pdf}
\includepdf[pages=-]{appendix.pdf}
\end{document}

withpypdf.py

from pypdf import PdfReader, PdfWriter
letterhead = PdfReader("testbriefkopf.pdf").pages[0]
writer = PdfWriter(clone_from="dinbrief2.pdf")
for page in writer.pages:
    page.merge_page(letterhead, over=False)  # here set to False for letterhead
writer.write("withletterhead.pdf")