It's possible to be idempotent without being side-effect free. If you PUT some record, for example, then that operation _will_ have side effects (modifying the record). If you then PUT that same data again, the result will be the same (it's idempotent).
that’s not a side effect. in common usage, a side effect is an extra action, not the desired action itself. if you PUT some record, and some other record or state changes,
that’s a side effect.
I don't disagree with common usage, but common usage is not what's being discussed here.
It is a side effect in programming usage (not just HTTP).
Something is side-effect-free if and only if the only result of it running is that you get an answer. If you ignore the answer, then you cannot tell you ran the function/method/call/whatever. PUT is not side-effect-free.
That said, side-effect-free-ness is an incomplete paraphrasing of the HTTP spec (RFC7231); you'll notice that the only mentions of the phrase "side effect" are giving examples of legal side effects.
