[chore] Standardize linting across the workspace

[ThreeLight2000]

Motivation

The workspace exposes root lint and verify commands, but lint coverage is not consistent across packages. The current ESLint and Prettier setup is concentrated in apps/client-raycast, while other workspace packages do not yet have a shared, clearly documented lint baseline.

This makes quality checks vary by package and can leave the root Turbo lint task with incomplete coverage.

Scope

• Inventory JavaScript and TypeScript packages and their current lint/formatting needs.
• Choose and document the workspace linting baseline, including the relationship between ESLint and Prettier.
• Add shared configuration where appropriate while preserving package-specific requirements such as the Raycast config.
• Add a lint script to each applicable package, or document why a package is intentionally excluded.
• Ensure the root pnpm lint and pnpm verify commands cover the intended source packages through Turbo.
• Exclude generated, build, dependency, and other non-source artifacts from linting.
• Document local lint and auto-fix commands in the contributor guidance.
• Integrate the standardized lint checks into the repository verification/CI workflow.

Acceptance criteria

• The supported package set and linting baseline are documented.
• Every applicable source package has a working lint command.
• Root linting covers all intended packages and fails on lint errors.
• Existing Raycast-specific linting continues to work.
• Generated and dependency artifacts are not linted.
• Contributor documentation explains how to run and fix lint issues.
• Repository verification passes with the new lint coverage.

Verification plan

• Run pnpm lint from the workspace root.
• Run pnpm verify.
• Exercise linting for each supported package, including apps/client-raycast.
• Confirm generated output and dependency directories are excluded.
• Verify that an intentional lint violation fails the relevant package and root commands.