chore(ui): refactor workspace to monorepo (#70)

## Summary by Sourcery

Refactor the UI project structure into a pnpm monorepo packages layout
and align tooling and automation with the new paths.

Enhancements:
- Reorganize the UI app from the root ui directory into packages/ui
within a pnpm workspace.
- Update pnpm workspace configuration to include all packages under
packages/*.
- Adjust paths in changeset configuration so the @dropout/ui package
resolves from packages/ui.

Build:
- Update pre-commit configuration paths and arguments to reflect the new
UI location and normalize hook argument formatting.
- Update Dependabot configuration so npm updates target /packages/ui
instead of /ui.

CI:
- Update GitHub Actions workflows to watch packages/** instead of ui/**
and to run frontend tasks from packages/ui.
- Update pnpm cache dependency paths in workflows to use the root
pnpm-lock.yaml.
- Simplify frontend install steps in test workflows to run from the
repository root.

Chores:
- Add a new index.html under packages/ui and remove the old
ui/index.html to match the new project layout.

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