How can I run a second wp_remote_post() based on the response of the first?

wp_remote_post has a configuration option called blocking. Its description says:

Whether the calling code requires the result of the request.
If set to false, the request will be sent to the remote server, and processing returned to the calling code immediately, the caller will know if the request succeeded or failed, but will not receive any response from the remote server. Default true.

Since the default value is true, you can expect the call to block until a response is received. Therefore, the first request should complete before the second.

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