Grounding Requirements for same structure subpanel
Your ground path is through the EMT conduit. It needs a proper connection to the main panel ground and to the sub panel ground. You could use grounding bushings, but standard EMT connectors meet code.

The “connections” to the concrete reinforcing are not part of a normal grounding or bonding approach. This kind of bond is only used at the service entrance and uses more substantial wire.

One concern with your installation is that EMT conduit can corrode in buried or embedded installations. I have seen conduit rusted completely away after four or five decades of service. This can result in high ground impedance and non-tripping breakers. If you have this problem you should run a new feeder with a proper ground connection. Do not drive a separate ground rod at the subpanel. The ground connection belongs at the service to avoid ground loops and to ensure over current protective devices work properly.