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>

clients/tui/src/App.tsx

@@ -887,8 +887,15 @@ function App({
   // Disconnect handler
   const handleDisconnect = useCallback(async () => {
     if (!selectedServer) return;
-    await disconnectInspector();
-    // InspectorClient will update status automatically, and data is preserved
+    try {
+      await disconnectInspector();
+      // InspectorClient will update status automatically, and data is preserved
+    } catch (err) {
+      // Nothing above this catches: the only caller is the key handler, which
+      // cannot await. Surface the failure the same way handleConnect does
+      // rather than letting it escape as an unhandled rejection.
+      setConnectError(err instanceof Error ? err.message : String(err));
+    }
   }, [selectedServer, disconnectInspector]);
 
   const handleClearOAuth = useCallback(async () => {
@@ -1428,12 +1435,15 @@ function App({
         input.toLowerCase() === "c" &&
         (inspectorStatus === "disconnected" || inspectorStatus === "error")
       ) {
-        handleConnect();
+        // Both handlers own their failures internally (each ends in a catch
+        // that surfaces the message), so there is nothing left for a key
+        // handler — which cannot await — to do with the promise.
+        void handleConnect();
       } else if (
         input.toLowerCase() === "d" &&
         (inspectorStatus === "connected" || inspectorStatus === "connecting")
       ) {
-        handleDisconnect();
+        void handleDisconnect();
       }
     }
   });

clients/tui/src/components/PromptsTab.tsx

@@ -53,8 +53,10 @@ export function PromptsTab({
         if (selectedPrompt.arguments && selectedPrompt.arguments.length > 0) {
           onFetchPrompt(selectedPrompt);
         } else {
-          // No arguments, fetch directly
-          (async () => {
+          // No arguments, fetch directly. The IIFE catches everything it can
+          // throw, so there is no rejection for this key handler — which
+          // cannot await — to own.
+          void (async () => {
             try {
               const invocation = await inspectorClient.getPrompt(
                 selectedPrompt.name,

clients/tui/src/components/ResourcesTab.tsx

@@ -186,7 +186,9 @@ export function ResourcesTab({
       }
     };
 
-    fetchContent();
+    // An effect body is synchronous, and fetchContent already catches
+    // everything it can throw, so there is no rejection left to own.
+    void fetchContent();
   }, [shouldFetchResource, inspectorClient, onAuthRecoveryRequired]);
 
   const listWidth = Math.floor(width * 0.4);