Possible to have both Wi-Fi and Ethernet connected to the same network?

As you have found out, from the routing perspective, while possible, it is not ideal to have addresses from the same network in different interfaces.

Routing expects a different network per interface, and ultimately one of them will take precedence over the other in routing, since they overlap.

The advised solution for having more than one interface connected to the same network is to aggregate them together in a bridge interface.

The bridge interface will "own" the IP address, and the actual real interfaces are grouped as a virtual single entity under br0.

allow-hotplug eth0
iface eth0 inet manual

allow-hotplug wlan0
iface wlan0 inet manual

auto br0
iface br0 inet dhcp
    bridge_ports eth0 wlan0

Debian Linux: Configure Network Interfaces As A Bridge / Network Switch