The L3 agent scheduler extension (l3_agent_scheduler) allows retrieve mappings between Neutron routers and L3 agents.

API doc:
https://docs.openstack.org/api-ref/network/v2/?expanded=list-l3-agents-hosting-a-router-detail#l3-agent-scheduler
Source code:
https://github.com/openstack/neutron/blob/fefd9a6bb1e5b685d56c75e7a538b0dfc0a959ec/neutron/db/l3_hascheduler_db.py#L44-L55