The terms are being confused sadly which is causing an issue. There's WCFS (Windows Clustering Foundation Services) which FCI (Failover Cluster Instance) runs on and requires shared disks. An AlwaysOn AG can also run on WCFS but it uses non shared storage and provides live read only replicas.
In other words A FCI is a shared storage architecture and you fail over from node to node. FCI doesn't in any way provide a 'read only' solution out of the box. Usually you will do mirroring+snapshot/log shipping or something else if you only have FCI. Right now what you are doing is simply adding another failover node, not an AlwaysOn AG.
This is what you are looking for (from the link). Note the multi node cluster with shared storage and the non shared storage AG:
Right now this is what you're doing. You're simply adding a 3rd node to the shared storage cluster:
This guide works well if you already have a FCI and want to add AG to it. Just look for how to install an AG. I would go through the steps for you but there's a lot of steps and you're better off going with an actual guide with screenshots and such. Do you have somewhere to test this in? Have you tried an Azure instance to test with if not? I would not recommend doing this live to prod. Here is some good documentation from Microsoft. Are you also sure that your code is AG compliant?
If you use MSDTC or cross db transactions you could create a serious problem.
Now the bigger question is are you the person who will be supporting this and is this prod? It seems like it's important because you're utilizing both FCI and AGs. I would highly suggest you research FCI and AGs in depth before deploying to prod. There are tons of resources out there. I would highly recommend not attempting to push this through on prod with the current understanding. You might set yourself up for major failure and your HA solution can bring you down.