aibridge: Automated CLI testing for AI Bridge clients

## Problem

AI Bridge supports multiple clients (Claude Code, Codex CLI, Copilot CLI, etc.). New releases of either AI Bridge or these clients can silently break compatibility. We currently have no automated way to detect these regressions and often discover them only after users report issues. When new features are introduced, we need to manually test clients to guarantee that nothing broke.

## Proposal

Design and implement an automated testing strategy to detect AI Bridge client incompatibilities quickly, at least for clients that support CLI automation. It should be possible to run these tests manually.

Write a small RFC that defines which clients can be automated, what test scenarios to run, the infrastructure, provider key configuration, and cadence for running them, and how failures get reported.