The unmanaged switch, as it seems you already know, cannot be used with VLANs.
Have you replaced the unmanaged switch with this new managed one?
Start with the router. The additional networks will be created on the router along with the appropriate firewall rules (and typically also a DHCP server). Each network will be associated with a VLAN on the router's lan port. The new networks will be tagged.
Then, the switch will be configured with the same 3 VLANs as are present on the router's lan port -- this will apply for the port that connects to the router, as well as the 3 ports that connect to the APs. These are called trunks (a port/cable that carries multiple networks). I would also recommend that you create an access (a 'normal', one network, untagged) port for each of the networks on the switch so that you can test that is functioning properly with a wired computer.
Finally, you'll setup your APs with the same VLAN trunk configuration on the port that connects to the switch. You'll then make 2 new unmanaged network interfaces and then create two new SSIDs that you will connect to those new networks.
Start by creating just one new network and get it working end-to end. Then you can use the same recipe to create the final one.
You can use this tutorial to setup a new network on the router. Skip the wifi part, of course. When you've got everything else done, post the config here (specific instructions below) and we'll review and show you how to setup the VLAN on the lan port.
Please connect to your OpenWrt device using ssh and copy the output of the following commands and post it here using the "Preformatted text </> " button:
Remember to redact passwords, MAC addresses and any public IP addresses you may have:
ubus call system board
cat /etc/config/network
cat /etc/config/dhcp
cat /etc/config/firewall
