Improve server_start execution time

[afharo]

As a follow up to #108950 where we noticed that server_setup doubled its execution time in the past 30 days, affecting Kibana's total startup time, we now want to pay attention to any improvements we can apply to server_start to reduce the consistent 5s it takes to run:

After #108950, this step takes approx 1/3 of Kibana's total startup time.

APM data shows that most of the time is spent establishing the Elasticsearch connection and opening the HTTPS port:

^Probably pointing to an issue with the SSL handling? 🤔

[elasticmachine]

Pinging @elastic/kibana-core (Team:Core)

[lizozom]

Closing for now. We will reopen if and when we have telemetry on this.