With http you can do it elegantly with a 429 and retry-after. 100% doing it at the edge is the way to go. The machinery which determines how long to delay a client's retry can benefit from knowledge of internal services' state, but I agree the ultimate decision must lie with the serving layer. That's the only way to efficiently deal with misbehaving clients.
On that note, one of the more memorable incidents of my career was when a 10M+ node client decided to retry as hard as possible on 4xx. That was fun x_x.
[edit] that is to say, for this mechanism to be robust your retry-after enforcement mechanism needs to be capable of withstanding almost every single one of your users attempting to illegally retry as fast as they physically can without negatively impacting that one user requesting legitimate traffic. https://media.tenor.com/p3mss3YI6TcAAAAM/wat.gif
I'm not proposing doing any exponential backoff retries, or even retries at all for internal services.
In my mind, the retries with exponential backoff and jitter belong only on the end-client(VSCode in this case). Everything else -> fail fast.