[Discover] Background search inspect in child flyout

[akowalska622]

Summary

Resolves: #242240
A-la-carte: https://akowalska622-pr-250252-discover-background-search-inspect-i.kbndev.co/

This pull request refactors and modernizes the way flyouts are implemented and opened in the search session management UI. The main improvements include extracting and reusing the InspectFlyout component, switching to the new openSystemFlyout API for overlays, and simplifying context and rendering logic. Additionally, the "Inspect" action is now available in the session management table and renders a connected background search details as a child flyout.

Steps to test:

1. Install kibana_sample_data_ecommerce data
2. Switch to ES|QL
3. Run FROM kibana_sample_data_ecommerce | LIMIT 1 | EVAL delay(5000ms)
4. While query is running, click Send to background button (adjust delay if you need more time)

5. Click three dots on app bar and select Background searches option

6. Click three dots on any background search entry and select Inspect

7. Details should be displayed in a child flyout

Checklist

Check the PR satisfies following conditions.

Reviewers should verify this PR satisfies this list as well.

• Any text added follows EUI's writing guidelines, uses sentence case text and includes i18n support
• Documentation was added for features that require explanation or tutorials
• Unit or functional tests were updated or added to match the most common scenarios
• If a plugin configuration key changed, check if it needs to be allowlisted in the cloud and added to the docker list
• This was checked for breaking HTTP API changes, and any breaking changes have been approved by the breaking-change committee. The release_note:breaking label should be applied in these situations.
• Flaky Test Runner was used on any tests changed
• The PR description includes the appropriate Release Notes section, and the correct release_note:* label is applied per the guidelines
• Review the backport guidelines and apply applicable backport:* labels.

Identify risks

Does this PR introduce any risks? For example, consider risks like hard to test bugs, performance regression, potential of data loss.

Describe the risk, its severity, and mitigation for each identified risk. Invite stakeholders and evaluate how to proceed before merging.

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[akowalska622]

Context is handled in src/core/packages/overlays/browser-internal/src/flyout/system_flyout_service.tsx now

[kertal]

just came by to be exited ... would have helped me a lot in the debugging phase of 8.2, so my wish now it having a Time Machine, to backport the commit to September 2025

[akowalska622]

/ci

[akowalska622]

Opening for review again, maybe this time we have more luck 🤞 🍀

[AlexGPlay]

maybe we can just use IconType from eui

[akowalska622]

Good idea, swapped in 77abf2a

[AlexGPlay]

lgtm - played with it for a bit and now it works nice! 🚀

[andrimal]

Code changes LGTM! ✨ Nothing touches Lens or visualizations.

[elasticmachine]

💚 Build Succeeded

• Buildkite Build
• Commit: 47db00e

Metrics [docs]

Module Count

Fewer modules leads to a faster build time

id	before	after	diff
data	625	628	+3

Page load bundle

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

id	before	after	diff
data	442.8KB	442.6KB	-236.0B

History

• 💚 Build #426351 succeeded 465dd68
• 💔 Build #426260 failed 68da902
• 💚 Build #425639 succeeded 406e9f1
• 💔 Build #425613 failed 7468bd2
• 💔 Build #425515 failed e83c3c7
• 💛 Build #399416 was flaky 0604f1f

cc @akowalska622