[7.x] [Search] Integrate "Send to background" UI with session service (#83073)

[Dosant]

Backports the following commits to 7.x:

• [Search] Integrate "Send to background" UI with session service ([Search] Integrate "Send to background" UI with session service #83073)

[kibanamachine]

💚 Build Succeeded

• continuous-integration/kibana-ci/pull-request
• Commit: 462c59b

Metrics [docs]

Module Count

Fewer modules leads to a faster build time

id	before	after	diff
dashboard	185	186	+1
data	600	603	+3
dataEnhanced	38	37	-1
total			+3

Async chunks

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

id	before	after	diff
dashboard	193.3KB	197.3KB	+4.0KB
dataEnhanced	26.5KB	27.7KB	+1.3KB
discover	431.6KB	433.6KB	+2.0KB
total			+7.2KB

Page load bundle

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

id	before	after	diff
dashboard	321.4KB	322.3KB	+951.0B
data	976.8KB	985.9KB	+9.1KB
dataEnhanced	35.2KB	35.1KB	-121.0B
discover	81.8KB	82.1KB	+213.0B
total			+10.1KB

Saved Objects .kibana field count

Every field in each saved object type adds overhead to Elasticsearch. Kibana needs to keep the total field count below Elasticsearch's default limit of 1000 fields. Only specify field mappings for the fields you wish to search on or query. See https://www.elastic.co/guide/en/kibana/master/development-plugin-saved-objects.html#_mappings

id	before	after	diff
background-session	5	7	+2

To update your PR or re-run it, just comment with:
@elasticmachine merge upstream