[7.x] [Search Session] Fix integration in vega, timelion and TSVB (#87862)

[Dosant]

Backports the following commits to 7.x:

• [Search Session] Fix integration in vega, timelion and TSVB ([Search Session] Fix integration in vega, timelion and TSVB #87862)

[kibanamachine]

💚 Build Succeeded

• continuous-integration/kibana-ci/pull-request
• Commit: 7ece422

Metrics [docs]

Page load bundle

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

id	before	after	diff
data	1006.3KB	1006.4KB	+138.0B
dataEnhanced	39.4KB	39.4KB	+39.0B
visTypeTimelion	34.8KB	36.3KB	+1.5KB
visTypeTimeseries	137.1KB	137.6KB	+484.0B
visTypeVega	60.5KB	60.7KB	+137.0B
total			+2.3KB

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