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>

.github/copilot-instructions.md

@@ -11,6 +11,7 @@ The Inspector ships as one package with three clients (**Web**, **CLI**, **TUI**
 - **Avoid double casts (`as unknown as T`).** They erase all type safety and usually mean the real type is being worked around. Prefer a type guard, a narrower single cast, or fixing the underlying type. If genuinely unavoidable (a documented gap in a third-party type, or bridging structurally-identical shapes TS can't relate), it **must** carry an inline comment justifying why it's safe and why nothing better exists. An unjustified `as unknown as` is not acceptable in review.
 - Prefer inference, type guards, and precise annotations over assertions.
 - An `_` prefix is the intentionally-unused marker (`argsIgnorePattern` / `varsIgnorePattern` / `caughtErrorsIgnorePattern`).
+- **Never float a promise.** `@typescript-eslint/no-floating-promises` is `error` in all five ESLint scopes, so every promise must be awaited, `.catch(…)`-terminated, returned, or explicitly discarded with `void`. Prefer **holding and settling** it — a floated rejection surfaces in an unrelated file as an SDK-internal stack, which is how two un-held `callTool` calls failed the whole `npm run ci` chain (#1947). Reach for `void` only when the callee already owns its failures (it ends in a `catch`) or the caller genuinely cannot await (a sync effect body, an Ink key handler), and say which in a comment. In Storybook play functions, `expect(...)` from `storybook/test` is instrumented and returns a promise — it must be awaited.
 
 ## React and UI (web client)