I understand that for most members of this community this is offensively primitive, but I have spent an hour ploughing through all APIs, so until https://github.com/mocnik-science/osm-python-tools/issues/70 is fixed perhaps it helps somebody:

# From URL (e.g., "https://www.openstreetmap.org/way/30722274#map=14/49.2925/38.1815")
# to geo-URI of the center of the object: geo:49.2953098,38.1827257

import os.path
import sys
import urllib.parse
from OSMPythonTools.cachingStrategy import CachingStrategy, JSON
from OSMPythonTools.api import Api
from shapely.geometry import shape

CachingStrategy.use(JSON, cacheDir=os.path.expanduser("~/.cache/osm"))

api = Api()

parsed_url = urllib.parse.urlparse(sys.argv[1])
way = api.query(parsed_url.path)
geom = shape(way.geometry())
print(f"geo:{geom.centroid.y:.7f},{geom.centroid.x:.7f}")

Complete program is now hosted at https://sr.ht/~mcepl/osm_where/