mdfdefinestyle{infobox}{
    innertopmargin=1em,
    innerbottommargin=1em,
    backgroundcolor=cyan!30
}

documentclass{article}
usepackage[utf8]{inputenc}
usepackage[T1]{fontenc}
usepackage{lipsum}
usepackage{tikz}

setlength{parindent}{0pt} % Wenn Absatzabstand, dann Einzug unnötig
setlength{parskip}{1.5em}

usetikzlibrary{tikzmark}
makeatletter
newififaddmarks

gdef @makecol {%
    ifvoidfootins
    ifaddmarks
    setbox@outputbox vbox{%
        boxmaxdepth @maxdepth
        pgfmark{startofthepage}%
        unvbox @cclv
        @tempskipalastskip unskippgfmark{endofthepage}vskip@tempskipa
    }%
    else
    setbox@outputbox box@cclv
    fi
    else
    setbox@outputbox vbox {%
        boxmaxdepth @maxdepth
        ifaddmarkspgfmark{startofthepage}fi%
        unvbox @cclv
        ifaddmarks@tempskipalastskip unskippgfmark{endofthepage}vskip@tempskipafi
        vskip skipfootins
        color@begingroup
        normalcolor
        footnoterule
        unvbox footins
        color@endgroup
    }%
    fi
    let@eltrelax
    xdef@freelist{@freelist@midlist}%
    global let @midlist @empty
    @combinefloats
    ifvbox@kludgeins
    @makespecialcolbox
    else
    setbox@outputbox vbox to@colht {%
        @texttop
        dimen@ dp@outputbox
        unvbox @outputbox
        vskip -dimen@
        @textbottom
    }%
    fi
    global maxdepth @maxdepth
}

usepackage{fancyhdr}
pagestyle{fancy}
chead{%
    ifaddmarks
    tikz[overlay,remember picture]
    draw[black,fill=cyan!30]
    ([xshift=-2pt]pic cs:startofthepage)
    rectangle
    ([xshift=linewidth+2pt,yshift=-2pt]pic cs:endofthepage);
    fi
}

begin{document}

    addmarkstrue

    lipsum*[1-2] bböööböfootnote{A footnote}

    lipsum*[1-2]footnote{A longer footnote which needs a bit more space on the bottom of this page.}

    lipsum*[1-2]footnote{Some footnote}

    newpageaddmarksfalse %needed to avoid a gray empty page because of the splitted footnote

end{document}