Because I can't know for sure now, I would test using network namespaces if it's possible to use the failover IPs without effect on the "main" IP. I can improve this answer depending on results: I suspect ARP issues caused by "ARP flux" (ie when one interface answers an ARP request on behalf of an other) because of the multiple interfaces on the same LAN.
So I'd remove the additional failover IP settings and would manually run this as root, to use those IP in network namespaces, which will isolate the host from any network issue:
Create namespaces:
ip netns add failover1
ip netns add failover2
Move additional interfaces to namespaces (and stop if this fails):
ip link set eno2 netns failover1 || echo 'No support. stop here.'
ip link set eno3 netns failover2
Configure...
ip -n failover1 link set lo up
ip -n failover2 link set lo up
ip -n failover1 link set eno2 up
ip -n failover2 link set eno3 up
ip -n failover1 address add Failover_IP_1 peer 89.163.138.65 dev eno2
ip -n failover1 route add default via 89.163.138.65
ip -n failover2 address add Failover_IP_2 peer 89.163.138.65 dev eno3
ip -n failover2 route add default via 89.163.138.65
This can work because the provider already ran settings on the gateway to have routes for those additional IPs on the same LAN.
Now the failover addresses should be pingable, without any side effect on server (But there's no service nor firewall set on the network namespaces owning those IPs).
You can run commands from them (but depending on settings, no service might mean no DNS, if the DNS server was running on the host):
ip netns exec failover1 traceroute -n 8.8.8.8
Delete namespaces (which will bring back interfaces to host, as long as nothing was left running in those namespaces):
ip netns delete failover1
ip netns delete failover2
So did it work as described for now?