Great answer from @potong. I'm commenting here since it doesn't fit into a comment.
I ended up with the following script:
export PRIVKEY=/etc/letsencrypt/live/mydomain.de/privkey.pem
export FULLCHAIN=/etc/letsencrypt/live/mydomain.de/fullchain.pem
export CERT=/etc/letsencrypt/live/mydomain.de/cert.pem
sed -E \
-e '/CAChain = \[/{:a;N;/\];/!ba
s/(= \[).*(\];)/\1$(cat $FULLCHAIN \| sed \'s/^.*CERTIFICATE//\' )\2/
s/.*/echo "&"/e}' \
-e '/PrivateSecureKey = \[/{:a;N;/\];/!ba
s/(= \[).*(\];)/\1$(cat $PRIVKEY \| sed \'s/^.*CERTIFICATE//\' )\2/
s/.*/echo "&"/e}' \
-e '/SecureCertificate = \[/{:a;N;/\];/!ba
s/(= \[).*(\];)/\1$(cat $CERT \| sed \'s/^.*CERTIFICATE//\' )\2/
s/.*/echo "&"/e}' \
file_to_edit
I need to add a preprocessing of the file to embed, sinces it starts with undesired lines.
I'm getting 6: Syntax error: ")" unexpected.