sql server – Cannot connect to MSSQL using kerberos auth

We have a standalone SQL server (Microsoft SQL Server 2019 (RTM) – 15.0.2000.5 (X64)) that we’d like to use kerberos authentication with, to enable querying of other databases via linked servers. We’ve set up our MSSQL instance to run using an AD service account and given that account access to the private key for the SSL cert that the instance uses for connection encryption.

After restarting, I see in the ERRORLOG that MSSQL is able to register the appropriate SPNs:

Server      The SQL Server Network Interface library successfully registered the Service Principal Name (SPN) ( MSSQLSvc/mssql-server.example.org ) for the SQL Server service.
Server      The SQL Server Network Interface library successfully registered the Service Principal Name (SPN) ( MSSQLSvc/mssql-server.example.org:1433 ) for the SQL Server service.

However, when connecting via SSMS (v18.9.2) and then checking the auth_method I see:

/*------------------------
SELECT net_transport, auth_scheme FROM sys.dm_exec_connections WHERE session_id = @@SPID;
------------------------*/
net_transport                            auth_scheme
---------------------------------------- ----------------------------------------
TCP                                      NTLM

(1 row affected)

Looking at the documentation I’ve found on the web, I believe I’ve done everything necessary to make this work. Any ideas what I’ve missed?