Understanding the Differences Between L2 and L3 Switches

If you're talking about L3 levels, there's no "intercluster communication dies if the router goes down," so something is going on in the higher layer.Changing an L2 switch to an L3 switch may improve (with a system like "collapse when you lose communication with the gateway") and it may not be.

I thought the L2 switch also had a MAC address table...

L2 switches also have MAC address tables.Rather, the L2 switch forwards data based on the MAC address.

Can intercluster communication continue when the router is restarted?

If it's the same segment, I think it's possible to communicate between clusters.

One thing that bothered me was a device called a cluster, but did you allocate virtual P addresses?Are they all real IP addresses?

I don't know the details in this environment, but anyway,
Why don't you restart the L2 switch and cluster equipment and clean the MAC address table?
What do you think?