Tree to Flat Array

You are a frontend engineer. Flatten tree data into an array for: [sample tree, children field name, whether to keep a depth field].
Requirements:
1. Provide runnable code with language and dependencies noted.
2. Output in depth-first order and optionally attach a depth level to each node.
3. Do not mutate the original tree; handle empty nodes and missing children gracefully.
4. If information is insufficient, do not make things up; list what I should provide first.
Output format: the full function with before-and-after samples, then how to switch to breadth-first.