Deprecate EuiBetaBadge

[weronikaolejniczak]

Summary

This PR:

• adds internal wrapper components for the docs for beta (BetaBadge) and deprecation (DeprecatedBadge) purposes,
• reuses BetaBadge and DeprecatedBadge across the documentation website,
• marks EuiBetaBadge as deprecated,
• removes EuiBetaBadge from a11y ESLint rules and utils,
• replaces EuiBetaBadge with EuiBadge in EuiCard and EuiKeyPadMenuItem.

Relates to #9343

API Changes

component / parent	prop / child	change	description
EuiCard	betaBadgeProps	Changed	Type changed from EuiBetaBadgeProps to EuiBadgeProps. Use children instead of label. Tooltip props moved to betaBadgeTooltipProps.
EuiCard	betaBadgeTooltipProps	Added	New prop (Omit<EuiToolTipProps, 'children'>) that wraps the badge in an EuiToolTip when content or title is provided. Replaces tooltipContent, tooltipTitle, and anchorProps from the old EuiBetaBadgeProps.
EuiKeyPadMenuItem	betaBadgeLabel (internal)	Changed	Badge now rendered using EuiBadge instead of EuiBetaBadge. Letter-only badges (no betaBadgeIconType) get a circular style via new euiKeyPadMenuItem__betaBadgeLetter CSS. Public props unchanged.

Screenshots

Before	After
{Before image}	{After image}

Impact Assessment

• 🔴 Breaking changes — What will break? How many usages in Kibana/Cloud UI are impacted?
• 💅 Visual changes — May impact style overrides; could require visual testing. Explain and estimate impact.
• 🧪 Test impact — May break functional or snapshot tests (e.g., HTML structure, class names, default values).
• 🔧 Hard to integrate — If integration is complex, stage commits in Kibana/Cloud UI branches for cherry-picking and link to them below.

Impact level: 🔴 High

Release Readiness

• Documentation: {link to docs page(s)}
• Figma: {link to Figma or issue}
• Migration guide: {steps or link, for breaking/visual changes or deprecations}
• Adoption plan (new features): {link to issue/doc or outline who will integrate this and where}

QA instructions for reviewer

Checklist before marking Ready for Review

• Filled out all sections above
• QA: Tested light/dark modes, high contrast, mobile, Chrome/Safari/Edge/Firefox, keyboard-only, screen reader
• QA: Tested in CodeSandbox and Kibana
• QA: Tested docs changes
• Tests: Added/updated Jest, Cypress, and VRT
• Changelog: Added changelog entry
• Breaking changes: Added breaking change label (if applicable)

Reviewer checklist

• Approved Impact Assessment — Acceptable to merge given the consumer impact.
• Approved Release Readiness — Docs, Figma, and migration info are sufficient to ship.

[elasticmachine]

💔 Build Failed

• Buildkite Build
• Commit: e570c36

Failed CI Steps

• :docusaurus: Build and deploy documentation website

cc @weronikaolejniczak

[elasticmachine]

💔 Build Failed

• Buildkite Build
• Commit: e570c36

Failed CI Steps

• 🔨 EUI pull request test

cc @weronikaolejniczak