Function execute_plan 

pub fn execute_plan(
    root: &Path,
    plan: &Plan,
    _old_lock: &Lock,
    check: bool,
) -> Result<Lock>

Execute a sync plan: write target files and return the updated lock.

• Create / Update: writes the rendered content to disk.
• Orphan: deletes the target file.
• Conflict: returns error (caller must resolve conflicts first).
• UpToDate: skips.

If check is true, performs a dry-run — returns the new lock without writing anything. Returns Err if there are unresolved conflicts.