Update dependencies: stencil and supporting packages (track work on `update-dependencies` branch)

[seanwuapps]

Purpose

This issue will track the work to update Stencil and other repository dependencies on the update-dependencies branch, validate the component suite, and ensure the docs and examples still build and render correctly.

Scope

• Update Stencil to the target version (document chosen version and rationale).
• Update major/critical dependencies (list below as you pick them).
• Run builds for packages (core, docs, apps) and fix any compile/runtime regressions.
• Run unit tests, E2E / Playwright tests, and visual regression checks where applicable.
• Update docs/examples and changelog entries if APIs or behavior change.

Checklist

• Pin target Stencil version and add notes
• Update package.json dependencies (core packages + devDeps)
• Install and run a full repo build (packages + docs)
• Run unit tests (jest) and fix failures
• Run Playwright/E2E tests and fix failures
• Run style/lint checks and fix warnings/errors
• Run visual diff (if configured) and inspect screenshots
• Update docs/examples where relevant
• Create follow-up PRs for fixes and component updates

Branch

Work is happening on the update-dependencies branch.

Notes

• If you want me to automate parts of this (CI runs, branch PRs, or test scripts), tell me which checks to run first.

Assigned

Assigning to the branch owner to pick up: @seanwuapps