I tried replicating the set up on a different OpenWrt device set up with only a LAN interface(basically a switch behind a Google WiFi router) and have not had success. The handshake succeeds, but the OpenWrt device seems to not be able to send any data to the peer.
Are you sure? It can appear to be handshaking but not actually working. The way to find out for sure is to issue the following command on your OpenWrt router after WG has been running for 1 minute or longer (so you can see if you get persistent handshakes, just the initial one, or none):
wg show
Please post the output here (for all output, redact private information like the public/private keys, public IPs, etc. -- make it clear what you've redacted to avoid confusion, and please do not redact/change RFC1918 IP addresses).
Also post the contents of the following files:
/etc/config/network
/etc/config/firewall
You've still left out a lot of the information that I had requested... it's really hard to help without that information.
You might consider changing this from a dumb AP mode device to a standard router (NAT+firewall) in a double NAT configuration and then just allowing forwarding from wg > wan. This works well in my experience.
This is incorrect. If you are trying to pass an entire subnet, you need to address the tunnel devices differently. Otherwise, only specify a single /32 IP from 192.168.2.0/24 for peers.
Is there a reason that you are providing such sparse details? it would be so much easier to understand what does and does not work if you would post the entire contents of the firewall and network config files, the output of wg show, and details about which ping tests actually work. It could also be useful to understand exactly how things are connected (sounds like LAN-LAN for the main router-OpenWrt connection) and if there is a reason you need it to be in a dumb ap type config.
That said, based on the extremely limited info you've provided, you need to change your android peer to 192.168.2.2/32. This should exactly match the address of the wg peer config as @lleachii suggested for the OpenWrt side.
Unless there is a reason you must run the OpenWrt router in dumb ap mode, I will again point out that configuring the OpenWrt router as a normal NAT+firewall device (i.e. default) behind your primary router (Google Wifi) will work really well. This is, as I mentioned before, what I do.
You will connect a cable between your Google Wifi (LAN) and your OpenWrt (WAN), set a static IP or a static DHCP assignment for the OpenWrt WAN (on the Google Wifi subnet) and configure port forwarding for your WG port. Configure WireGuard on your OpenWrt device, open the port in the firewall, and configure a wg zone in the firewall. Allow forwarding from WG > WAN and you're done. I can guarantee that this method works as long as you configure it properly.