feat: add CUJ2 inference demo chat UI and update CUJ2 instructions

[yuanchen8911]

Summary

Add a browser-based chat UI for testing Dynamo inference deployments and update CUJ2
documentation with chat UI instructions.

Motivation / Context

Provides a simple way to interactively test Dynamo vLLM inference deployments via a
browser chat interface, in addition to the existing curl-based approach.

Fixes: N/A
Related: N/A

Type of Change

• Bug fix (non-breaking change that fixes an issue)
• New feature (non-breaking change that adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update
• Refactoring (no functional changes)
• Build/CI/tooling

Component(s) Affected

• CLI (cmd/eidos, pkg/cli)
• API server (cmd/eidosd, pkg/api, pkg/server)
• Recipe engine / data (pkg/recipe)
• Bundlers (pkg/bundler, pkg/component/*)
• Collectors / snapshotter (pkg/collector, pkg/snapshotter)
• Validator (pkg/validator)
• Core libraries (pkg/errors, pkg/k8s)
• Docs/examples (docs/, examples/)
• Other: ____________

Implementation Notes

• examples/demos/workloads/inference/chat.html — Browser chat UI targeting
  Dynamo's OpenAI-compatible /v1/chat/completions endpoint
• examples/demos/workloads/inference/chat-server.sh — Single script that starts
  kubectl port-forward and a local proxy server, then serves the chat UI on port 9090
• examples/demos/cuj2.md — Updated "Test the endpoint" section with chat UI as
  Option 1 and curl as Option 2

Testing

make lint

Tested manually against Dynamo vLLM deployment on H100 EKS cluster.

Risk Assessment

• Low — Isolated change, well-tested, easy to revert
• Medium — Touches multiple components or has broader impact
• High — Breaking change, affects critical paths, or complex rollout

Rollout notes: N/A

Checklist

• Tests pass locally (make test with -race)
• Linter passes (make lint)
• I did not skip/disable tests to make CI green
• I added/updated tests for new functionality
• I updated docs if user-facing behavior changed
• Changes follow existing patterns in the codebase
• Commits are cryptographically signed (git commit -S) — GPG signing info

[mchmarny]

/lgtm