DLC: Git Ops

Automated git hygiene — clean up merged branches, prune stale remote tracking refs, and verify repository state.

Step 1: Sync with Remote

Fetch latest state, prune deleted remote branches, and sync the default branch.

# Detect the default branch dynamically
# 2>/dev/null suppresses errors when symbolic-ref is not set (e.g. shallow clone)
DEFAULT_BRANCH=$(git symbolic-ref refs/remotes/origin/HEAD 2>/dev/null | sed 's|refs/remotes/origin/||')