Why are footcite and printbibliography interpreting the author differently?

The correct input for simple names with only given and family name parts is either

• <Given> <Family> as in

  Emma Sigfridsson
  

• or <Family>, <Given> as in

  Sigfridsson, Emma
  

See also How should I type author names in a bib file?.

So all the names in the example entries are switched in the input. The correct entries would be

@book{Stephan2005,
  author   = {Anke Stephan},
  title    = {Erinnertes Leben: Autobiographien, Memoiren
              und Oral-History-Interviews als historische Quellen},
  year     = {2005},
  location = {München},
}
@online{Ammerer2011,
  author  = {Heinrich Ammerer and Elfriede Windischbauer},
  editor  = {Zentrum polis – Politik Lernen in der Schule},
  title   = {Kompetenzorientierter Unterricht in Geschichte
             und Politischer Bildung: Diagnoseaufgaben mit Bildern},
  year    = {2011},
  url     = {https://www.ph-online.ac.at/phst/voe_main2.getVollText?pDocumentNr=64434&pCurrPk=3902},
  urldate = {2020-07-21},
}

This wasn't immediately obvious for me in the Stephan2005 entry (because both Anke and Stephan could be the given name), but it is quite clear for Ammerer2011.

With that input we get

The reason is that biblatex tries to use the 'natural' name order <Given> <Family> as much as possible. Since names are traditionally sorted in <Family>, <Given> order, however, biblatex uses that order for the first name in the bibliography so that the word that determines the sorting position in the bibliography is the first. See Why a comma appears for the first author of the bibliography? for more discussions about the background.

Specifically, the code responsible for that is from biblatex.def

DeclareNameAlias{default}{given-family}
DeclareNameAlias{sortname}{family-given/given-family}

from authortitle.bbx

DeclareNameAlias{author}{sortname}
DeclareNameAlias{editor}{sortname}
DeclareNameAlias{translator}{sortname}

and from verbose.cbx

newbibmacro*{cite:full}{%
  usebibmacro{cite:full:citepages}%
  printtext[bibhypertarget]{%
    usedriver
      {DeclareNameAlias{sortname}{default}}
      {thefield{entrytype}}}%
  usebibmacro{shorthandintro}}

This means that normally (default) biblatex uses the format given-family. But for author, editor and translator at the beginning of an entry, it uses sortname, which is family-given/given-family. Yet in the full citation of your verbose sortname is explicitly reset to the natural default format.

So you should be able to modify all name formats to your wishes by redefining the name formats sortname and default and/or by dropping or changing DeclareNameAlias{sortname}{default} in the definition of cite:full.

If I understand correctly the following might come closer to what you want

documentclass[ngerman]{article}
usepackage[T1]{fontenc}
usepackage[utf8]{inputenc}
usepackage{babel}
usepackage{csquotes}

usepackage[style=verbose, backend=biber]{biblatex}

% <Family> <Given> order
DeclareNameAlias{default}{family-given}
DeclareNameAlias{sortname}{default}

% no comma
renewcommand*{revsdnamepunct}{}

% to distinguish FAMILY and Given name better
renewcommand*{mkbibnamefamily}{textsc}

begin{filecontents}{jobname.bib}
@book{Stephan2005,
  author   = {Anke Stephan},
  title    = {Erinnertes Leben: Autobiographien, Memoiren
              und Oral-History-Interviews als historische Quellen},
  year     = {2005},
  location = {München},
}
@online{Ammerer2011,
  author  = {Heinrich Ammerer and Elfriede Windischbauer},
  editor  = {Zentrum polis – Politik Lernen in der Schule},
  title   = {Kompetenzorientierter Unterricht in Geschichte
             und Politischer Bildung: Diagnoseaufgaben mit Bildern},
  year    = {2011},
  url     = {https://www.ph-online.ac.at/phst/voe_main2.getVollText?pDocumentNr=64434&pCurrPk=3902},
  urldate = {2020-07-21},
}
end{filecontents}
addbibresource{jobname.bib}

begin{document}
nullvfill % only for this example
Lorem autocite{Stephan2005}
ipsum autocite{Ammerer2011}
printbibliography
end{document}

---

Not directly related to the question, but on second glance, the entry Ammerer2011 might be better represented as a @collection. After all Heinrich Ammerer and Elfriede Windischbauer are editors (Herausgeber) and not authors.

@collection{Ammerer2011,
  editor     = {Heinrich Ammerer and Elfriede Windischbauer},
  title      = {Kompetenzorientierter Unterricht in Geschichte
                und Politischer Bildung: Diagnoseaufgaben mit Bildern},
  year       = {2011},
  publisher  = {Zentrum polis – Politik Lernen in der Schule},
  location   = {Wien},
  url        = {https://www.ph-online.ac.at/phst/voe_main2.getVollText?pDocumentNr=64434&pCurrPk=3902},
  urldate    = {2020-07-21},
}

For Stephan2005 @book looks a bit unusual as well. I'd be inclined to make it a @report.

@report{Stephan2005,
  author   = {Anke Stephan},
  title    = {Erinnertes Leben: Autobiographien, Memoiren
              und Oral-History-Interviews als historische Quellen},
  year     = {2005},
  type     = {Digitales Handbuch zur Geschichte und Kultur Russlands und Osteuropas},
  number   = {10},
  doi      = {https://doi.org/10.5282/ubm/epub.6270},
  location = {München},
}