Embeddable persistable state migration

[Dosant]

In scope of #74352 we added .telemetry .extract and .inject functions to embeddable service which can take in any embeddable input and perform associated action on it.
Same set was added to dynamic actions of uiActionsEnhanced and drilldowns. All of those where connected together.

Similar to that approach we need to add a way to migrate persistable state on embeddable input. As phase 1 we need to at least add it on server side and run as part of SO migrations.

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Needed for: #71409
Part of: #63358

[elasticmachine]

Pinging @elastic/kibana-app-arch (Team:AppArch)

[Dosant]

The open question we have right now:

With migrate functionality we want to follow similar approach like we did with extract, inject and telemetry (#74352). This approach relies on a chain of registries and enhancement pattern:

migrate() on a drilldown -> registers in DynamicActionsRegistry on uiActionsEnhanced -> used in EmbeddableEnhanced (x-pack) -> enhances embeddable plugin in OSS -> can be invoked by EmbeddableStart['migrate'].

With current approach to invoke a migration chain on embeddable you'd call a function on EmbeddableStart.
But SO migrations have to be registered in SETUP phase.

So right now seems there is no way to connect plugin persistable state migration system we plan have and a SO migration that has to be registered in setup phase.

[ppisljar]

we can register migrations in the setup phase even if specific migrations rely on start contract of another plugin, but migrations would need to run AFTER start phase of all plugins has finished (and those start contracts are actually available). In setup phase we would pass a promise of start services in (core.getStartServices())

[Dosant]

As discussed on services sync:

We will expose inject, extract, migrate methods on plugins start and will assume it is called only AFTER setup and that every plugin already registered everything. Core runs migrations after all plugins finished their setup phase. No additional APIs or changes from platform are needed.

[Dosant]

Closed by #82296