Run dependency updates daily

[anth-volk]

Fixes #604

Summary

• Run dependency updates once daily at 3:00 PM US Eastern time.
• Use America/New_York so the schedule follows daylight-saving changes.
• Reuse the existing update-dependencies pull request and append commits without rewriting its active review history.
• Merge current main into the update branch before regenerating clients and upgrading every package lockfile.
• Prevent overlapping dependency-update runs.
• Keep branch preparation, commit/push handling, and PR creation in dedicated shell scripts rather than inline workflow blocks.

Validation

• bash -n .github/scripts/dependency-update-*.sh
• shellcheck .github/scripts/dependency-update-*.sh
• actionlint .github/workflows/update-dependencies.yml
• git diff --check
• Confirmed the workflow detects the existing update PR, Update dependencies #583.
• Confirmed the current update branch incorporates current main without conflicts.