I don’t know what a “background task” is. The response to a particular request provided by your endpoint must be replicable. Given the nature of the Anthropic API, I assume it is not replicable, which may explain the need for a proxy. However, if it is replicable, then ensure that an idempotency key and IPv6 are used.
For future improvements that may not require replicated calls and that also support IPv4, refer to this thread: Announcing Two Major Upgrades for HTTPS Outcalls: IPv4 Support + Non-Replicated Calls are now LIVE!