What is the best dynamic routing protocol?

Question

linux

To put it a bit simplistically, the problem is as follows. There are several physical Linux servers with two network adapters and two switches, each of which is connected to one of the servers' ethernet ports. Switches switch subnets 172.16.1.0/24 and 172.16.2.0/24, each of which has servers with IP addresses. Also, on each of the servers, a local ip-address is assigned, not tied to a specific network adapter, from the range 172.16.0.0/24, with a /32 mask (by creating a bridge to which physical interfaces were not added).

You need to choose a dynamic routing protocol that will ensure the availability of all local ip in 172.16.0.X from each of the servers, with a minimum rebuild time (preferably no more than 10 seconds) in case of partial loss of connectivity, and present "out of the box" in FRR packets or bird.
Unfortunately, using Bonding / LACP in a particular case will not work, so you have to look for how to provide the ability to failover at a higher level.

Answer 1

Switches switch subnets 172.16.1.0/24 and 172.16.2.0/24, each of which has servers with IP addresses.

Do you have L2 / L3 switches and are they configured for routing to L3? If so, then you need to look at the configuration switches, because they are hinges between different networks. If they work for you on L2, then you have full access.