Maybe it's not a very elegant solution and it's based on the method of answering question: https://gis.stackexchange.com/a/295348/120129.
It's one of the variants of solving your question, set up a geoinstrument (for me it's a road with the name "road_border" 11 m wide, type - line (MultiLineString)),
run a geoinstrument :-),
WITH
tbla AS (SELECT id, ((ST_DumpPoints(geom)).geom) geom FROM road_border),
tblb AS (SELECT (ST_Buffer((ST_Dump(geom)).geom, 0.0001)) geom FROM tbla),
tblc AS (SELECT ST_Centroid(ST_UnaryUnion(Unnest(ST_ClusterWithin(geom, 0.0001)))) geom FROM tblb),
tbld AS (SELECT ((ST_Dump(ST_DelaunayTriangles(ST_Collect(geom)))).geom) geom FROM tblc),
tble AS (SELECT (ST_Boundary(geom)) geom FROM ST_Dump((SELECT ST_Polygonize(geom) geom FROM (SELECT ST_Union(geom) geom FROM
(SELECT ST_ExteriorRing(geom) geom FROM tbld) AS lines) AS foo))),
tblf AS (SELECT ST_MakeLine(p1, p2) geom FROM (SELECT ST_PointN(geom, generate_series(1, ST_NPoints(geom)-1)) p1,
ST_PointN(geom, generate_series(2, ST_NPoints(geom))) p2 FROM tble) AS geom),
tblg AS (SELECT ST_Buffer((ST_Dump(ST_Union(ST_Buffer(geom, 0.0005)))).geom, -0.0005) geom FROM road_border)
SELECT ST_Intersection (a.geom, b.geom) geom FROM tblf a JOIN tblg b ON ST_Within(a.geom, b.geom);
and see the result.
Good luck to everyone :-),
Original solutions ...
This script is called - ST_RoadAxisFromDelaunayTriangulation...
