[Logs / Metrics UI] [NP followup] Only use plugin start contracts in the UI

[Kerry350]

This discussion provides context for this ticket.

We should, once possible, move to only using ClientPluginsStart. And remove merging of setup and start. This, however, relies on the usageCollection plugin making reportUiStats available in start first.

[elasticmachine]

Pinging @elastic/logs-metrics-ui (Team:logs-metrics-ui)