[Embeddables][Serialized State Only] Use serialized state in state transfer service

[Heenawter]

Fixes #213153

Summary

This PR ensures that the embeddable state transfer service exclusively uases serialized state. Previously, the transfer service accepted either runtime state or serialized state - but we are in the process of removing the concept of "runtime state" for embeddables (at least as far as the Dashboard is concerned), and this is one step towards that goal.

Note that this PR is built off the subset of "embeddable state transfer service related" changes from #215416 - all I did was clean up these changes, finalized some of the cases that were missed in the original draft, and updated tests as necessary.

Checklist

• Unit or functional tests were updated or added to match the most common scenarios
• The PR description includes the appropriate Release Notes section, and the correct release_note:* label is applied per the guidelines

[elasticmachine]

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Metrics [docs]

Module Count

Fewer modules leads to a faster build time

id	before	after	diff
aiops	605	606	+1

Public APIs missing comments

Total count of every public API that lacks a comment. Target amount is 0. Run node scripts/build_api_docs --plugin [yourplugin] --stats comments for more detailed information.

id	before	after	diff
embeddable	131	132	+1

Async chunks

Total size of all lazy-loaded chunks that will be downloaded as the user navigates the app

id	before	after	diff
aiops	452.1KB	452.7KB	+651.0B
canvas	1017.1KB	1017.1KB	+28.0B
cases	1.3MB	1.3MB	+13.0B
dashboard	542.6KB	542.5KB	-81.0B
lens	1.4MB	1.4MB	+169.0B
maps	3.0MB	3.0MB	+74.0B
ml	5.4MB	5.4MB	+105.0B
slo	921.7KB	921.8KB	+42.0B
synthetics	985.8KB	985.8KB	+21.0B
visualizations	342.2KB	342.4KB	+224.0B
total			+1.2KB

Page load bundle

Size of the bundles that are downloaded on every page load. Target size is below 100kb

id	before	after	diff
embeddable	20.5KB	20.5KB	+10.0B

Unknown metric groups

References to deprecated APIs

id	before	after	diff
dashboard	13	11	-2