Detect and classify relay errors via x-relay-error header

[zoedsoupe]

Problem

JS checks x-relay-error header to distinguish gateway errors from function errors. Elixir treats all errors generically.

Proposed Solution

{:error, %{type: :relay_error, code: :unauthorized}}  # Gateway issue
{:error, %{type: :http_error, code: :not_found}}     # Function error
{:error, %{type: :network_error}}                     # Connection issue

Benefits

• Better error diagnosis
• Distinguish gateway vs function errors
• Inform retry strategies
• Feature parity with JS

JS Reference: functions-js/src/FunctionsClient.ts:119-128