Spike: Keep Pod Log Output Current Using Automated Artifact Generation

## Description

Example documentation in pepr-excellent-examples may include pod log output snippets. Like code snippets (see #191), these logs can become outdated when the examples change. We should research automated solutions to keep pod logs current, potentially using GitHub Actions artifacts to share logs between repositories.

**Current state:**
- Pod log output (if included) is manually copied into documentation
- No automated verification that logs match current example behavior
- Logs can become stale as examples evolve

**Problems:**
- **Manual maintenance** - Developers must manually run examples and copy log output
- **Documentation drift** - Easy to forget to update logs when examples change
- **No validation** - No way to verify logs are accurate for current code
- **Time-consuming** - Running examples to capture logs is tedious

**Proposed solution (requires research):**

**Option 1: GitHub Actions Artifacts (cross-repo)**
1. Add workflow to pepr-excellent-examples that runs each example
2. Capture pod logs as artifacts
3. pepr-docs build downloads artifacts and extracts logs
4. Inject logs into documentation during build

**Challenges:**
- Cross-repository artifact access complexity
- Artifact retention limits (90 days default)
- Authentication/permissions between repos
- Timing coordination (when to generate artifacts)

**Option 2: Commit logs to pepr-excellent-examples**
1. GitHub Actions in pepr-excellent-examples runs examples
2. Captures logs and commits them to repo (e.g., `logs/` directory)
3. pepr-docs reads logs during build like it reads READMEs
4. Simpler than artifacts, but adds noise to git history

**Option 3: On-demand generation in pepr-docs**
1. pepr-docs build process runs examples locally
2. Captures logs in real-time during build
3. No cross-repo complexity
4. Requires Kubernetes cluster access during build (problematic for CI/CD)

**Option 4: Manual with validation**
1. Keep logs in pepr-excellent-examples manually
2. Add CI check that validates logs match current output
3. Fails if logs are outdated
4. Less automated but simpler to implement

## Related Files

- https://github.com/defenseunicorns/pepr-excellent-examples (external repository)
- https://github.com/defenseunicorns/pepr-docs/blob/main/scripts/index.mjs
- https://github.com/defenseunicorns/pepr-docs/blob/main/.github/workflows/docs.yml
- https://github.com/defenseunicorns/pepr-docs/blob/main/.github/workflows/test.yml

## Definition of Done

We've considered our options and learned more about the problem. Perhaps we've even come up with an alternative idea!

**Benefits (if implemented):**
- Always current log output in documentation
- Reduced manual maintenance
- Confidence that examples work as documented
- Better user experience with accurate examples

**Risks:**
- High implementation complexity for potentially low value
- Cross-repo dependencies could make builds fragile
- Artifact retention limits could cause build failures
- May be over-engineering if logs rarely change