Just did some basic testing on broadcast addresses using socat, broadcast is not working at all with /32 addresses. With /24 addresses, broadcast only reaches nodes that share a subnet. Nodes that don't share the subnet aren't reachable by broadcast even when they're reachable via unicast.

Edit1: Did more testing, it seems like broadcast traffic ignores routing tables.

On 192.168.0.2, I am running socat -u udp-recv:8000,reuseaddr - to print UDP messages.

Case 1: add 192.168.0.1/24

# ip addr add 192.168.0.1/24 dev eth0
# # Testing unicast
# socat - udp-sendto:192.168.0.2:8000 <<< "Message"
# # Worked
# socat - udp-sendto:192.168.0.255:8000,broadcast <<< "Message"
# # Worked

Case 2: Same as above but delete 192.168.0.0/24 route

# ip addr add 192.168.0.1/24 dev eth0
# ip route del 192.168.0.0/24 dev eth0
# # Testing unicast
# socat - udp-sendto:192.168.0.2:8000 <<< "Message"
2024/02/13 22:00:23 socat[90844] E sendto(5, 0x5d3cdaa2b000, 8, 0, AF=2 192.168.0.2:8000, 16): Network is unreachable
# # Testing broadcast
# socat - udp-sendto:192.168.0.255:8000,broadcast <<< "Message"
# # Worked

Third: with your /24 subnet you told your system it has that many address to talk to. With the /32 you told it has none to talk to. With adding a route you gave the additional info „there is another network called … with a subnet of … wich you can talk to“ So your second solution is more or less equivalent but with extra steps. I don’t know how it’s implemented in the backend but it is different as in the second there is no network per default but you add routes to some. In contrast to there is a network and no routing is needed

This isn't actually correct. An ip address assignment for a host with an IP requires both the address and the subnet mask. One cannot be assigned without the other. Even more strictly speaking the address by itself isn't useful to the network stack except as a destination, and isn't used anywhere in the network stack of the host. There is always a subnet mask, sometimes the mask is assumed to be /32 (255.255.255.255), sometimes /24, whatever. But whenever you are talking about assigning an ip address to any IP speaker, it must include the mask.

The routing table on every IP speaker will include at a minimum a single host-route. That is the IP of the system itself with a /32 mask and the configured interface of that IP. Whether it's eth0, a bonded interface, a loopback etc.

Once you have that single host route, additional routes can be added as needed. These routes require an address, a subnet, and a next-hop. The next hop can be a directly attached interface, or an IP that the is reachable by another route in the host routing table.

If you have only a host route, as OP has, then the system has no network knowledge, so there are no reachable next hop IPs. So you would have to use a directly connected interface, like the OP did. Once you tell the system 192.168.0.0/24 is reachable through that interface, then any IP Packets that have that network as their destination will use that interface with a source of the one IP it has. In the case of two servers connected back to back, assuming the other server knows where the source of the packet came from, there is no problem sending traffic back.

So to answer the OPs question, there is no difference between one host route, then a static route pointing to an interface, and just a directly connected interface with your server IP on it. They are two different routes that may have different administrative distances, but assuming you aren't doing anything exotic, for all intents and purposes they are the same.

If you are talking about layer2 concepts like broadcasts, the host-route configured server can still receive broadcasts, but only broadcasts with destination ip of 255.255.255.255, not scoped broadcasts like 192.168.0.255 since it will ignore all traffic that isn't unscoped broadcast or a full match to it's own IP address.

With your /32 assignments you basically told your system, it has no network to talk to

More accurately you've told the device that it is the only device on its network. It's a network of 1 IP with no broadcast nor network ID. This is very common with public IPs where you get a singular IP.