Run Base project checks in Banyan Labs CI

[codeforester]

Problem

Banyan Labs is the natural real-project proof for Base, but the repo does not yet have a concrete issue to run Base-managed project checks in GitHub Actions. The broad CI/CD phase tracker #35 captures the theme; this issue captures the closable Base integration slice.

Desired outcome

After basectl ci lands in basefoundry/base#525, add a Banyan Labs GitHub Actions path that runs Base project checks for the repo and produces structured CI output.

Scope

• Install or otherwise make Base available in the CI job using the supported release or checkout path chosen for the workflow.
• Run basectl ci check banyanlabs --format json once Implement basectl ci as a non-interactive CI entry point base#525 is available.
• Consider basectl ci doctor banyanlabs --format json if the output is useful and stable for CI logs.
• Keep ordinary Banyan validation, Go tests, build checks, and API smoke tests in the workflow alongside the Base checks.
• Document any Base prerequisites the workflow must install before invoking basectl ci.

Non-goals

• Do not implement basectl ci in this repository.
• Do not replace Banyan Labs service-level tests with Base checks.
• Do not block this on future Java, Python, Kubernetes, or supply-chain phases.

Acceptance criteria

• A GitHub Actions workflow runs Base checks for Banyan Labs on pull requests or the main validation path.
• The workflow fails on Base error findings and preserves warnings as non-fatal diagnostics.
• The workflow output includes JSON suitable for later parsing or artifact capture.
• The workflow still runs the repo-local validation and URL shortener tests expected by Banyan Labs.

Validation

• Confirm the workflow passes on a clean branch after Base support is available.
• Confirm a deliberately broken Base manifest or missing required tool produces a clear CI failure.

Demo impact

This is the visible 1.0.0 proof: Banyan Labs can depend on Base in CI, not only on a developer workstation.