[Embeddable] Improve explicit input handling

[dokmic]

Background

The current implementation is not as straightforward as it could be. The current implementation holds the state of all the child items in the container. This diverges child implementation into two separate paths when it is inside a container and is self-sufficient.
The merged state is hard to debug, and sometimes it is confusing where the state is coming from.
Resolving this should guarantee support of the nested containers.

Proposal

The base embeddable implementation should be updated to hold its own state regardless of context. The container implementation should be updated accordingly to gather children's states and combine that in the same format as the current implementation.
All methods handling explicit and the default state should be updated to match the existing behavior.

Notes

• Data access should be bi-directional. For example, filters should go down from the dashboard to the single embeddable.
• It might be achieved by providing children and parent getters to walk up and down the tree.
• It is better to approach that by doing an offline exploration and creating a PoC that passes the existing CI pipeline.

[elasticmachine]

Pinging @elastic/kibana-app-services (Team:AppServicesUx)

[elasticmachine]

Pinging @elastic/kibana-presentation (Team:Presentation)

[ThomThomson]

Closing this in favour of the Embeddables Rebuild initiative.