docs: show the decline branch in the lead input_required example

[yy5652-hash]

docs: show the decline branch in the lead input_required example

What

The first input_required example a developer meets, in the inputRequired JSDoc (packages/core-internal/src/shared/inputRequired.ts) and at the top of docs/servers/input-required.md (examples/guides/servers/input-required.examples.ts#registerTool_inputRequired), tests only for an accepted answer:

const confirmed = acceptedContent(ctx.mcpReq.inputResponses, 'confirm', confirmationSchema);
if (confirmed?.confirm !== true) {
    return inputRequired({ ... });
}

acceptedContent returns undefined for a declined or cancelled answer just as it does on the first entry, so a decline makes the handler return inputRequired() again. The client re-asks on every retry until inputRequired.maxRounds, the operator is put the same question eight times, and then the call fails with "Multi-round-trip request 'tools/call' still required input after 8 rounds". The server sees no error at any point.

The guide already explains this further down ("Read the responses on re-entry") and inputResponse() exists for exactly this; the lead example just does not use it, and it is the one that gets copied. We copied it into a hackathon server and shipped the loop.

Change

• The lead example (JSDoc and guide) reads the response with inputResponse() first and finishes on any elicitation answer: accepted → act; declined or cancelled → an isError result. The request is only re-issued when nothing has arrived.
• One paragraph in the guide says why: acceptedContent alone cannot tell a refusal from a first entry.
• A test in packages/server/test/server/inputRequired.test.ts pins the one-round behaviour for decline and cancel on the 2026-07-28 era through the real server funnel, and records that acceptedContent reads both as undefined.

No runtime code changes; no changeset added. pnpm sync:snippets --check, the server and core-internal test suites and lint pass locally. The markdown page was not prettier-clean before this change (unrelated long lines), and that is left as it was.

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