Refactor the kube-scheduler configuration API, command setup, and server
setup according to the guidelines established in #32215 and using the
kube-proxy refactor (#34727) as a model of a well factored component
adhering to said guidelines.

* Config API: clarify meaning and use of algorithm source by replacing
modality derived from bools and string emptiness checks with an explicit
AlgorithmSource type hierarchy.
* Config API: consolidate client connection config with common structs.
* Config API: split and simplify healthz/metrics server configuration.
* Config API: clarify leader election configuration.
* Config API: improve defaulting.
* CLI: deprecate all flags except `--config`.
* CLI: port all flags to new config API.
* CLI: refactor to match kube-proxy Cobra command style.
* Server: refactor away configurator.go to clarify application wiring.
* Server: refactor to more clearly separate wiring/setup from running.

Fixes #52428.