No layer 2 traffic in an Open vSwitch bridge

I see no traffic in layer 2 and above in an OVS bridge, but I do see layer 1 traffic.

I have the following setup:

I have created a Linux VirtualBox VM with three adapters: NAT with port forwarding the internal SSH (22) port to external port, so that I can manage the VM, a bridged adapter to an ethernet cable connected an external machine (it could be a Raspberry PI or a laptop or ...etc.), and another bridged adapter to my RealTech Wifi dongle connected to my router. Inside the VM, I have created an OVS bridge between the latter two bridged adapters, with the intent of making the devices joined in the LAN to be also joined to my Wifi. I did it like the following:

ovs-vsctl add-br br0
ovs-vsctl add-port br0 <LAN bridged adapter inside the VM>
ovs-vsctl add-port br0 <Wifi bridged adapter inside the VM>

(I also disabled routing from the LAN and Wifi adapters inside the VM, and also disabled routing of the LAN inside the host, as I intend to access the device on the LAN using the wireless network)

There is no DHCP server from the LAN side, but of course there is one from the Wifi side. I have ran a DHCP discover from the device in the LAN and it acquired an IP address correctly and instantly from the router, which indicates that layer 1 packets are passing through just fine (also confirmed with Wireshark). However, I was not able to ping, for e.g., the router gateway itself or any device in the wireless network for that matter, including the bridge itself, and also nobody can ping that device in the LAN itself. I have checked Wireshark from the host side (not in VM) and it seems that ARP replies are being generated, but it doesn't seem to propagate across the bridge. I have tried multiple devices on the LAN to check that it is not the problem of the device connected to LAN itself.

Here is how I designed my network for a better representation:

I have also tried bare Linux bridges using brctl as well, and I experienced the same problem.

Ok, I found the answer after stumbling into another similar question: Layer 2 bridged networking issue with QEmu. I was able to pass traffic between the host, bridge VM, and network on the LAN, with enabling promiscuous mode. I tried changing the bridging adapter from Wifi to either a NAT (to send network to the device in LAN) or host only adapter (just for the sake of testing bridging). However, I was not able to ping the router outside when the bridge was attached to the Wifi adapter, and I guess this has to do with the driver not supporting bridging on the Wifi adapter.