Exercise 2: 502 vs. 504 — Possible Solution
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502 BAD GATEWAY
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Per this chapter, 502 means "a reverse proxy or gateway received an
invalid or malformed response from the backend it forwarded the
request to - the proxy itself is fine; its upstream isn't." The
backend DID respond - the response it sent back was simply invalid or
malformed in some way the proxy couldn't accept.

504 GATEWAY TIMEOUT
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Per this chapter, 504 means "a reverse proxy or gateway's upstream
never responded within the allowed time - distinct from 502, where the
upstream did respond, just invalidly." The backend did NOT respond at
all within the time the proxy was willing to wait.

WHAT EACH TELLS YOU ABOUT WHERE THE FAILURE HAPPENED
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Both point to the same general location - the connection between the
proxy/gateway and its own backend, not the connection between the
client and the proxy (which worked, since a response was received at
all). But they differ in what state the backend was in: 502 implies
the backend was reachable and processing but produced a broken
response (perhaps a crash mid-response, or a protocol mismatch); 504
implies the backend was either unreachable, overloaded, or simply too
slow to answer in time.

WHY THIS WORKS AS AN ANSWER
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It states the specific chapter definition of each code accurately, and
explains the concrete difference between "backend responded, but
invalidly" (502) and "backend never responded in time" (504) rather
than treating both as interchangeable "gateway problem" codes.