[7.x] [data.search.aggs] Move agg-specific field formats to search service (#69586)

[lukeelmers]

Backports the following commits to 7.x:

• [data.search.aggs] Move agg-specific field formats to search service ([data.search.aggs] Move agg-specific field formats to search service #69586)

[kibanamachine]

💚 Build Succeeded

• continuous-integration/kibana-ci/pull-request
• Commit: ec472ec

Build metrics

page load asset size

beta

id	value	diff	baseline
/bundles/app/core/bootstrap.js	-	-13.8KB	13.8KB
/bundles/core/core.entry.js	-	-1.1MB	1.1MB
/bundles/kbn-ui-shared-deps/[email protected]	-	-4.0MB	4.0MB
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/bundles/plugin/canvas/canvas.plugin.js	-	-2.0MB	2.0MB
/bundles/plugin/charts/charts.plugin.js	-	-833.9KB	833.9KB
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/bundles/plugin/console/console.plugin.js	-	-28.0KB	28.0KB
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/bundles/plugin/monitoring/monitoring.plugin.js	-	-22.8KB	22.8KB
/bundles/plugin/navigation/navigation.plugin.js	-	-122.2KB	122.2KB
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/bundles/plugin/observability/observability.plugin.js	-	-103.3KB	103.3KB
/bundles/plugin/painlessLab/painlessLab.plugin.js	-	-158.8KB	158.8KB
/bundles/plugin/regionMap/regionMap.plugin.js	-	-791.7KB	791.7KB
/bundles/plugin/remoteClusters/remoteClusters.plugin.js	-	-35.2KB	35.2KB
/bundles/plugin/reporting/reporting.plugin.js	-	-257.7KB	257.7KB
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/bundles/plugin/transform/transform.plugin.js	-	-21.6KB	21.6KB
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/bundles/plugin/uiActionsEnhanced/uiActionsEnhanced.plugin.js	-	-124.1KB	124.1KB
/bundles/plugin/upgradeAssistant/upgradeAssistant.plugin.js	-	-46.6KB	46.6KB
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/ui/fonts/inter_ui/Inter-UI-Regular.woff2	-	-86.4KB	86.4KB
total	-	-36.4MB	-

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