This documentation lists all the requirements
Connect to an Always On availability group listener
Read-only routing refers to automatically routing incoming listener
connections to a readable secondary replica that is configured to
allow read-only workloads.
Connections are automatically routed to the read-only replica if the
following are true:
At least one secondary replica is set to read-only access, and each
read-only secondary replica and the primary replica are configured to
support read-only routing.
The connection string references a database involved in the
Availability Group. An alternative to this would be the login used in
the connection has the database configured as its default database.
For more information, see this article on how the algorithm works with
The connection string references an availability group listener, and
the application intent of the incoming connection is set to read-only
(for example, by using the Application Intent=ReadOnly keyword in the
ODBC or OLEDB connection strings or connection attributes or
Since you already specify
ApplicationIntent in your connection query, you only need to check for the listener and the read-only routing list.
You can check the listener with this DMV:
from sys.availability_group_listeners as agl
And the read-only routing list with this snippet
ar.replica_server_name AS RoutingListOwner
, arr.replica_server_name AS ReadOnlyReplica
FROM sys.availability_read_only_routing_lists AS arorl
JOIN sys.availability_replicas AS ar
ON ar.replica_id = arorl.replica_id
JOIN sys.availability_replicas AS arr
ON arr.replica_id = arorl.read_only_replica_id
order by ar.replica_server_name, arorl.routing_priority