Add data tier removal guidance for self-managed and ECK

[eedugon]

Summary

• Add the data tier management and removal procedure for self-managed deployments and ECK, based on the existing ECH/ECE guidance.
• Apply the shared improvements to both guides while preserving deployment-specific orchestration and UI steps.

Main procedure improvements

• Rewrite the section introductions and preflight guidance to clearly distinguish regular indices, fully mounted snapshots, partially mounted snapshots, and mixed tiers.
• Clarify how _tier_preference, legacy require rules, and custom allocation filters affect relocation, including the difference between relocation triggered by index settings and by the deployment or orchestration plan.
• Make ILM handling safer by waiting for it to stop, reviewing policies before restart, and verifying its status and errors afterwards.
• Strengthen the searchable snapshot workflow with hidden-index discovery, support for non-standard names, snapshot and repository inventory, safer restore settings, restored-index verification, and optional source snapshot deletion with dependency warnings.
• Add clearer capacity, disk watermark, autoscaling, shard-monitoring, and final cluster-health checks.

Closes #6186

Validation

• git diff --check
• Vale (only existing or intentional Cloud terminology warnings)

[github-actions]

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🔍 Preview links for changed docs

• manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md
• manage-data/lifecycle/data-tiers/manage-data-tiers-self-managed-eck.md

[github-actions]

Elastic Docs Style Checker (Vale)

Summary: 2 warnings, 16 suggestions found

⚠️ Warnings (2): Fix when the suggestion improves clarity or correctness.

File	Line	Rule	Message
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	169	Elastic.Spelling	'substeps' is a possible misspelling.
manage-data/lifecycle/data-tiers/manage-data-tiers-self-managed-eck.md	153	Elastic.Spelling	'substeps' is a possible misspelling.

💡 Suggestions (16): Optional style improvements. Apply when helpful.

File	Line	Rule	Message
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	91	Elastic.WordChoice	Consider using 'deactivate, deselect, hide, turn off' instead of 'disable', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	97	Elastic.WordChoice	Consider using 'deactivate, deselect, hide, turn off' instead of 'disable', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	198	Elastic.WordChoice	Consider using 'deactivated, deselected, hidden, turned off, unavailable' instead of 'disabled', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	199	Elastic.WordChoice	Consider using 'deactivated, deselected, hidden, turned off, unavailable' instead of 'disabled', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	290	Elastic.WordChoice	Consider using 'deactivates, deselects, hides, turns off, makes unavailable' instead of 'disables', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	301	Elastic.WordChoice	Consider using 'deactivated, deselected, hidden, turned off, unavailable' instead of 'disabled', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	313	Elastic.WordChoice	Consider using 'deactivated, deselected, hidden, turned off, unavailable' instead of 'disabled', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	320	Elastic.WordChoice	Consider using 'deactivated, deselected, hidden, turned off, unavailable' instead of 'disabled', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	331	Elastic.WordChoice	Consider using 'deactivates, deselects, hides, turns off, makes unavailable' instead of 'disables', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	339	Elastic.WordChoice	Consider using 'deactivate, deselect, hide, turn off' instead of 'disable', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	426	Elastic.WordChoice	Consider using 'deactivate, deselect, hide, turn off' instead of 'disable', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	440	Elastic.WordChoice	Consider using 'deactivate, deselect, hide, turn off' instead of 'disable', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	444	Elastic.WordChoice	Consider using 'deactivated, deselected, hidden, turned off, unavailable' instead of 'disabled', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	446	Elastic.WordChoice	Consider using 'deactivated, deselected, hidden, turned off, unavailable' instead of 'disabled', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	456	Elastic.WordChoice	Consider using 'deactivated, deselected, hidden, turned off, unavailable' instead of 'disabled', unless the term is in the UI.
manage-data/lifecycle/data-tiers/manage-data-tiers-ech-ece.md	463	Elastic.WordChoice	Consider using 'deactivated, deselected, hidden, turned off, unavailable' instead of 'disabled', unless the term is in the UI.

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[eedugon]

@stefnestor : I'm adding you here as a reviewer because you also collaborated when we created the ECH/ECE version of the procedure.

Note that I didn't merge all into a single document because the resulting document would need a lot of applies switches and part of the narrative should be modified due to operational differences between Elastic Cloud + ECE and self-managed systems and ECK, but this could be evaluated in the future.

Also note that I found a few logical and technical caveats in the original procedure and I've tried to improve them.

Hoping you like the result Stef and @yetanothertw