server: slow server init times can result in process manager timeouts

**Describe the problem**

CockroachDB supports the [systemd readiness notification protocol](https://www.freedesktop.org/software/systemd/man/sd_notify.html).

We have observed that for clusters of a certain scale, initialization time can take a significant amount of time to complete (e.g. > 90s). Depending on how the process manager is configured, this can result in a situation where a node cannot restart and rejoin a cluster.

In cases where multiple nodes become unavailable at once, this can exacerbate unavailability and impeded recovery time.

A sanity check on the init process during startup, especially with large clusters, would be worthwhile here.

**Additional context**

Related to https://github.com/cockroachlabs/support/issues/2287.

Jira issue: CRDB-28416