Multi-homing: do i need Route metrics for 2 interfaces of which only one can access the internet?

I have 2 multi-homed servers which, besides each being connected to the Internet via one of their NICs, they are also connected back-to-back to each other via their 2nd NIC.

I use systemd-networkd to configure DHCP for the Internet links and Link-Local IPs for their cross-connection. The cross-connection config file looks like:

$ less /etc/systemd/network/25-other.network
[Match]
Name=eth5

[Network]
LinkLocalAddressing=yes

This works, and servers are assigned IPs like 169.254.245.165/16 on their secondary interfaces, respectively.

Not being very familiar with routing, I'm wondering if I can ever run into Internet connection issues due to routing. Does the kernel ever try to access the internet via the secondary interface? How is the decision made? I know route metrics can be used for this but unsure if I need them for my case (since no destinations are available via both interfaces), so do I need this?

[Network]
Metric=20

Or maybe this?

[Network]
RouteMetric=20

Edit: as the accepted answer says everything was fine without adding Routes. Posting the output of ip route if it helps anyone. It shows the default route going through my router and the 2nd route via the link-local IP.

default via 192.168.2.1 dev enp111s0 proto dhcp src 192.168.2.11 metric 1024 
169.254.0.0/16 dev enpa1a2 proto kernel scope link src 169.254.2.11 

Solution 1:

The OS uses the routing table netstat -rn to determine which interface to use. You probably have a default route that uses the "internet" interface. Unless you're doing something unusual, you don't need to mess with metrics.