I am not very familiar with this topic, but it seems that the tag highway=living_street is used only for roads marked with sign 5.34 — Residential Zone. In most cases, such a sign is absent, and the appropriate tags should be highway=service, service=*.
Perhaps someone more knowledgeable than me will join this discussion. Below are excerpts from the Resolution of the Cabinet of Ministers of Ukraine “On the Road Traffic Rules” — what I found related to residential zones (a machine translation):
1. GENERAL PROVISIONS
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1.10. Terms used in these Rules have the following meanings:
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bicycle — a vehicle, except wheelchairs, driven by the muscular power of a person located on it;
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residential zone — courtyard areas, as well as parts of settlements marked with road sign 5.34;
8. Traffic Regulation
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8.4. Road signs (Appendix 1) are divided into groups:
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g) informational and directional signs. They introduce or cancel certain traffic regimes and also inform road users about the location of settlements, various objects, and territories where special rules apply;
12. SPEED
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12.5. In residential and pedestrian zones, the speed must not exceed 20 km/h.
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26. TRAFFIC IN RESIDENTIAL AND PEDESTRIAN ZONES
26.1. Pedestrians are allowed to move in residential and pedestrian zones both on sidewalks and on the carriageway. Pedestrians have priority over vehicles but must not create unjustified obstacles to their movement.
26.2. In a residential zone, it is prohibited:
a) transit traffic of vehicles;
b) parking of vehicles outside designated areas and their placement in a way that obstructs pedestrian movement or the passage of emergency or special vehicles;
c) parking with the engine running;
d) driving instruction (training driving);
e) movement of trucks, tractors, self-propelled machines and mechanisms (except those servicing facilities and citizens, performing technological work, or belonging to citizens residing in this zone).
26.3. Entry into a pedestrian zone is permitted only for vehicles servicing citizens and enterprises located in that zone, as well as vehicles belonging to citizens who reside or work in that zone, or vehicles (motorized wheelchairs) marked with the identification sign “Driver with disability”, driven by drivers with disabilities or drivers transporting passengers with disabilities. If there are other access routes to the objects located in this area, drivers must use only those routes.
{Clause 26.3 as amended by Resolution of the Cabinet of Ministers No. 553 of 11.07.2018}
26.4. When exiting a residential or pedestrian zone, drivers must yield to other road users.
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33. ROAD SIGNS
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5. Informational and directional signs
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5.34 “Residential Zone”. Indicates entry into an area where special traffic conditions established by these Rules apply.
5.35 “End of Residential Zone”.