[Lens] Integrate search session id

[flash1293]

Related to #84908

To enable client side request caching and the "send to background" feature, an important piece of the puzzle is to manage a "search session id". It's created by const searchSessionId = searchService.session.start();. This id has to be kept around in the state and be passed to the currently running expression. Every time the user hits refresh, changes the filters or the search, a new session id has to be generated.

The state should be handled on frame level if possible and be passed down from there.

The session id doesn't have to be persisted.

[elasticmachine]

Pinging @elastic/kibana-app (Team:KibanaApp)