Linux

IP and Routing is layer 3, broadcast is layer 2 with Mac addresses being shared within a broadcast domain (often a vlan/lan) and the only requirement for layer 2 is a switch you don't need routers. Devices on a lan talk only via switches which switch based on Mac address tables. You don't learn Mac addresses of devices past your broadcast domain, that's what a router handles.

So in network practice (nothing Linux related) if you are on a broadcast network that's a /24 subnet, what should happen is all devices within that subnet talk to each other without using a router, instead they learn a mac address and the associated ip from a broadcast from the device which owns it.

If you tell your device that it's only on a /32 then it should discard every arp it hears as invalid. Which means it won't learn any neighbouring lan devices.

While your network on your single device with the /32 probably works ok to get to other networks (routed networks like internet or other vlans), because other networks ask the router, and the router probably learned your mac and ip on whatever vlan/interface your device is connected via.

But unless you're trying to do something unconventional, devices on a lan should match the routers expected subnet. This way devices can trust their assumption that within their subnet they communicate to other local devices by learning other network devices network address via arp, and communicate directly in unicast via learned ips from that arp. If it's outside the subnet they then look to the gateway. They trust the gateway. The gateway should route to the right interface or next hop.

If you really wanted to make this work though, usually routers can proxy arp. So in this case, you tell the router to 'oroxy' and broadcast your arp to other devices. Those devices on your lan looking for your ip will find the routers Mac address, then using destination network address translation you can redirect the incoming connection from a lan device to your device via your router. Then your /32 ip can probably work. Usually this is done when someone has put a static ip on a device with a wrong subnet ip on a vlan with another subnet. So the device which arps is ignored by the router and the other network devices. If you use the router to proxy arp you can basically give the local lan devices an ip to hit that they expect, which then you can translate to the misconfigured device. This generally is considered a bandaid solution temporary until a vendor or technician can fix their misconfiguration. I do not recommend.