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I was able to achieve my goal in overpass turbo by using the following lines of code:

/*
This has been generated by the overpass-turbo wizard.
The original search was:
“taxiway in airport ”
*/
[out:xml]/*fixed by auto repair*/[timeout:25];
// fetch area “airport” to search in
{{geocodeArea:LOWW}}->.searchArea;
// gather results
(
  // query part for: “aerodrome”
  node["aeroway"="aerodrome"](area.searchArea);
  way["aeroway"="aerodrome"](area.searchArea);
  relation["aeroway"="aerodrome"](area.searchArea);
 
  // query part for: “taxiway”
  node["aeroway"="taxiway"](area.searchArea);
  way["aeroway"="taxiway"](area.searchArea);
  relation["aeroway"="taxiway"](area.searchArea);
 
  // query part for: “taxilane”
  node["aeroway"="taxilane"](area.searchArea);
  way["aeroway"="taxilane"](area.searchArea);
  relation["aeroway"="taxilane"](area.searchArea);
 
  // query part for: “parking_position”
  node["aeroway"="parking_position"](area.searchArea);
  way["aeroway"="parking_position"](area.searchArea);
  relation["aeroway"="parking_position"](area.searchArea);
 
);
// print results
out meta;/*fixed by auto repair*/
>;
out meta qt;/*fixed by auto repair*/

EDIT: to make it work with overpy just run:

import overpy
api = overpy.Overpass()
r = api.query("""
/*
This has been generated by the overpass-turbo wizard.
The original search was:
“taxiway in airport ”
*/
[out:xml]/*fixed by auto repair*/[timeout:25];
// fetch area “airport” to search in
area[icao~"LOWW"]->.searchArea;
// gather results
(
  // query part for: “aerodrome”
  node["aeroway"="aerodrome"](area.searchArea);
  way["aeroway"="aerodrome"](area.searchArea);
  relation["aeroway"="aerodrome"](area.searchArea);
 
  // query part for: “taxiway”
  node["aeroway"="taxiway"](area.searchArea);
  way["aeroway"="taxiway"](area.searchArea);
  relation["aeroway"="taxiway"](area.searchArea);
 
  // query part for: “taxilane”
  node["aeroway"="taxilane"](area.searchArea);
  way["aeroway"="taxilane"](area.searchArea);
  relation["aeroway"="taxilane"](area.searchArea);
 
  // query part for: “parking_position”
  node["aeroway"="parking_position"](area.searchArea);
  way["aeroway"="parking_position"](area.searchArea);
  relation["aeroway"="parking_position"](area.searchArea);
 
);
// print results
out meta;/*fixed by auto repair*/
>;
out meta qt;/*fixed by auto repair*/
""")