The Responses client-tool restore raised an upstream function_call back to
custom_tool_call and tool_search_call without touching its item ID, so the
client received a custom_tool_call carrying the upstream's fc_ ID. That
combination is invalid: once the item lands in the client's history, any
later replay to an upstream that validates item IDs fails the whole request
with "Invalid 'input[N].id': 'fc_...'. Expected an ID that begins with
'ctc'", and every following message re-submits the same bad item.
Re-prefix the ID to match the type it is raised to, keeping the suffix so
the ID stays stable and unique per upstream item. IDs without a known
tool-call prefix are left alone rather than guessed at.
The lowering direction has to reverse this, because the WebSocket HTTP
bridge replays restored items back to the upstream and would otherwise lose
the upstream's own ID. normalizeLoweredFunctionItemID now maps a ctc_/tsc_
call ID back to fc_ instead of dropping it, which makes the round trip
lossless; output item IDs (ctco_/tso_) still have no function-protocol
counterpart and are still dropped. The helper was renamed from
dropInvalidLoweredFunctionItemID to match what it now does.
The stream restorer keeps the upstream ID for its own bookkeeping so later
upstream events still match the call, and emits the client-facing ID on
output_item.added/done and the custom_tool_call_input events.
Closes#6071
wucm667