ci: Harden background-agent MVP git authentication loop (#49373)

## Summary
- refresh git auth headers before each per-crash iteration in
`background_agent_mvp`
- add guarded `git fetch`/`git checkout` handling so one candidate auth
failure doesn’t fail the entire run

## Context
- fixes the auth failure seen in workflow run 22106378719 (`fatal: could
not read Username for 'https://github.com'`)
- related Linear issue: BIZOPS-853

## Testing
- ruby -e "require 'yaml';
YAML.load_file('.github/workflows/background_agent_mvp.yml')"

Release Notes:

- N/A

script/run-background-agent-mvp-local

@@ -147,7 +147,7 @@ Required workflow:
 2. Follow .factory/prompts/crash/investigate.md and write ANALYSIS.md
 3. Follow .factory/prompts/crash/link-issues.md and write LINKED_ISSUES.md
 4. Follow .factory/prompts/crash/fix.md to implement a minimal fix with tests
-5. Run validators required by the fix prompt for the affected crate(s)
+5. Run validators required by the fix prompt for the affected code paths
 6. Write PR_BODY.md with sections:
    - Crash Summary
    - Root Cause