[Nabil372]

Refs #4137

Why the change

After three SSE responses in a row that end within 1 s without being aborted, the client logs "SSE connections are closing immediately (possibly due to proxy buffering ...)" and long polls for the rest of the stream's life. It decides on duration alone (LiveState.handleSseConnectionClosed).

The server closes a live SSE request that is behind the log end as soon as it has sent the catch-up (do_serve_shape_log in api.ex). During a burst of writes each reconnect lands behind the log end, so three healthy responses end within milliseconds and the stream drops to long polling with nothing buffered. This is the second trigger in the #4137 comments, and it reproduces against a plain local Electric: a shape with liveSse: true, then a few hundred single-row inserts in separate transactions.

We run Electric with TanStack DB in production, in web apps and in Expo apps on iOS and Android, and any write-heavy moment can do this to every open SSE stream. We run a looser version as a patch on 1.5.28 (any short response that carried an event is exempt), which is only safe next to #4807's guard, so this PR also requires the response to have moved the offset.

The fix

A short response is exempt when its body delivered messages and the stream's offset after it differs from the offset the request was made at. An exempt response neither counts nor resets the counter and skips the short-connection backoff, so the next request goes out at once.

• Messages alone aren't enough: while an SSE up-to-date can move the offset back to ${lsn}_0 (TypeScript client: SSE up-to-date offset ${lsn}_0 regresses behind header electric-offset when the LSN carries multiple ops, causing an immediate-replay loop #4806), each response replays the same operations and closes at once, and the fallback with its backoff is what stops that loop today. The offset alone isn't enough either, because on main the header moves it when the response opens.
• A buffering proxy still trips the fallback: a body that ends before any event counts, and one whose buffered events arrive at the end took the server's full 60 s.
• This doesn't fix the CDN case in the original Live SSE short-connection fallback triggered by CDN cache-collapsed responses #4137 report, where collapsed bodies carry only keep-alive comments, hence "Refs".
• SseCloseInput (internal) gains a required advancedOffset (the offset changed, in either direction). SPEC.md gets constraint C10.
• fix(client): move the SSE offset only with an up-to-date #4836 touches the same finally block. After it, a body that ends before its up-to-date leaves the offset where it was and is followed by a long poll, so whichever lands second should also exempt hadUnflushedMessages; otherwise three catch-ups that each span a chunk boundary still fall back.

Tests

• shape-stream-state.test.ts: "short connection that advanced the offset leaves the counter unchanged" (fails on main).
• stream.test.ts, "SSE short-connection fallback": four catch-up responses that each carry a row and an up-to-date stay on SSE with no warning (fails on main); three short responses that replay operations and end back at 0_0 still fall back; three keep-alive-only bodies whose header moves the offset still fall back (fails if the header alone exempts a response, as does the existing integration test "should reset SSE fallback state after shape rotation (409)").

cd packages/typescript-client
pnpm run typecheck
pnpm run stylecheck
pnpm exec vitest run --config vitest.unit.config.ts   # 14 files, 456 tests pass

client.test.ts also passes against a local Electric (electricsql/electric:canary).