I think you may be confused here. You don't "add tags" with MQTT - they just show up in the Tag Browser automatically. Select the MQTT provider to see them.
"Browse Devices..." is for browsing the built in OPC server (or another connected OPC server).
Thank You! That worked!)
Something just went wrong with Ignition OPC UA Server after IT guys made some changes to network, so after the restart I changed the endpoint of this OPC Connection...