chore(lint): enable no-floating-promises in all five ESLint scopes

A floated promise is invisible at review time — the call reads like an
awaited one minus four characters — and the unhandled rejection it
produces surfaces in a different test, in a different file, as a stack
pointing at SDK internals. In #1947 two un-held `callTool` calls made
`npm run ci` unpassable and took a full investigation to attribute; the
fix was two lines. `@typescript-eslint/no-floating-promises` catches the
class outright, so enable it at `error` everywhere.

The rule is type-aware and `tseslint.configs.recommended` is not, so each
scope's config gains a parser project. The four clients name their own
tsconfig projects (both of them — `src` and `__tests__`/`server` live in
different ones). The root scope has no tsconfig at all, so add
`tsconfig.lint.json`: a lint-only project covering `core/**`,
`test-servers/src/**`, and `vitest.shared.mts`, emitting nothing and
gating nothing. It sets `moduleResolution: bundler` deliberately — under
NodeNext `core/`'s extensionless imports fail to resolve, every import
degrades to `any`, and the rule silently stops seeing promises at all.

Measured surface, and the fixes:

- core (2) — `stream.close()` in two Hono `onAbort` listeners. Hono
  invokes subscribers with a bare `subscriber()`, so a promise returned
  from the listener is floated one layer up; `closeAbortedStream` owns
  the rejection where it can actually be owned.
- tui (5) — `handleDisconnect` had no catch of its own and its only
  caller is a key handler that cannot await, so a failing disconnect was
  a live unhandled rejection; it now surfaces the message the way
  `handleConnect` does. The rest are `void` at callers that genuinely
  cannot await, over callees that already own their failures.
- web (92) — 83 are Storybook `expect(...)`, which is instrumented and
  returns a promise, now awaited (`scrollAreaStoryAssertions` is async
  for the same reason). Two tests were asserting against a provider call
  they never awaited. `open(url)` in both web servers now warns instead
  of escaping a synchronous callback.
- cli, launcher — already clean.

Type-aware linting costs time: `clients/web`'s `eslint .` goes from ~8s
to ~19s, inside `validate`. Narrowing the loaded projects is the lever if
that needs reducing later; dropping the rule is not.

Closes #1959

Signed-off-by: cliffhall <cliff@futurescale.com>

AGENTS.md

@@ -719,6 +719,12 @@ The ⚠️ option-deletion hazard, the snapshot rule, and the recovery recipe ab
 - Use type guards and type assertions to handle potential type mismatches and ensure type safety
 - Take advantage of TypeScript's advanced features like generics, type aliases, and conditional types to write more expressive and reusable code
 - Regularly review and refactor TypeScript code to ensure it remains well-structured and adheres to evolving best practices
+- **NEVER leave a promise floating.** `@typescript-eslint/no-floating-promises` is enabled at `error` in **all five** ESLint scopes — `clients/{web,cli,tui,launcher}` and the root `core/` + shared gate (#1959). Every promise must be awaited, returned, terminated with `.catch(…)`, or explicitly discarded with the `void` operator.
+  - **The class it catches is invisible at review time.** A floated call reads like an awaited one minus four characters, and the unhandled rejection it produces surfaces somewhere else entirely — a different test, a different file, a stack pointing at SDK internals. Two un-held `client.callTool(...)` promises made `npm run ci` unpassable in #1947: `disconnect()` rejected them with `Connection closed`, the unhandled rejection failed the whole vitest run, and the chain aborted at `coverage`, silently skipping `verify:build-gate`, `smoke`, and Storybook. Attributing it took a full investigation; the fix was two lines.
+  - **Prefer holding and settling the promise.** `void` is an escape hatch, not a fix — it is visible at review time (strictly better than nothing) but still discards the rejection. Reach for it only when the callee already owns its failures (it ends in a `catch` that surfaces the message) or the caller genuinely cannot await — a synchronous `useEffect` body, an Ink `useInput` key handler, a Hono `stream.onAbort` listener. Say **which** of those it is in a one-line comment; an unexplained `void` is a review finding. Where the callee does *not* own its failures, give it a `catch` rather than voiding the call (see `handleDisconnect` in `clients/tui/src/App.tsx`), or terminate with `.catch(…)` at the call site (see `open(url)` in `clients/web/server/{server,vite-hono-plugin}.ts`).
+  - **In Storybook play functions, `expect(...)` from `storybook/test` returns a promise.** Storybook instruments it so the interactions panel can trace each assertion, so every `expect` in a play function is awaited — as is any shared helper that wraps one (`src/test/scrollAreaStoryAssertions.ts` is `async` for this reason).
+  - **The rule is type-aware, so each scope's ESLint config carries a parser project.** The four clients point at their own tsconfig projects (both of them, since `src` and `__tests__`/`server` live in different ones); the root config points at **`tsconfig.lint.json`**, which exists solely to give the parser a program covering `core/**`, `test-servers/src/**`, and `vitest.shared.mts` — none of which is rooted in a tsconfig of its own. That file emits nothing and gates nothing: type *checking* for those sources stays where it was (`core/` through `clients/web`'s `tsc -b`, `test-servers/src` through `clients/cli`'s test project). It sets `moduleResolution: bundler` deliberately — `core/` uses extensionless relative imports, which NodeNext fails to resolve, degrading every import to `any` so the rule silently stops seeing promises at all. **When adding a first-party TS location to the root lint scope, add it to `tsconfig.lint.json`'s `include` too**, or the parser fails it outright with "was not found in any of the provided project(s)". Note also that a tsconfig `include` does **not** expand braces — `core/**/*.{ts,tsx}` matches nothing; list the extensions separately.
+  - Type-aware linting costs real time: `clients/web`'s `eslint .` went from ~8s to ~19s, and `lint` runs inside `validate`, the fast inner-loop check. That is the price of the guarantee; if it needs reducing later, narrowing the projects each scope loads is the lever, not dropping the rule.
 
 ## Web source layout: `src/lib` vs `src/utils`