fix: address Copilot review round 3 — conjunctive keywords, unflattenable allOf, branch inference

- rootUnion: a branch restating a constraint the root states differently is
  declined (keywords at one level are conjunctive and no intersection is
  computed here), while annotations may disagree freely. An `allOf` with a
  member it cannot fold in — JSON Schema's boolean form, or a $ref whose
  constraints are unknown rather than absent — is left intact instead of
  merged-and-stripped, which would turn an unsatisfiable schema into a
  fillable form.
- rootUnion: `declaresAnyFields` counts the raw composition members, so
  `hasInputFields` reports fields for a union the resolver declines and an
  App tool is never auto-invoked with empty arguments.
- SchemaForm: the picker opens on the branch the supplied values identify
  (an App deep link overlays its args, so they can name another branch), and
  a branch switch no longer carries a value the outgoing branch declared —
  the branches may type the same name differently.
- TUI: a base property some branch redeclares is offered in EVERY branch's
  section under that branch's inherited or specialized declaration, so a
  branch that does not redeclare it can still supply a required root
  argument.

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

clients/web/src/utils/toolUtils.ts

@@ -1,5 +1,5 @@
 import type { Tool } from "@modelcontextprotocol/client";
-import { resolveRootUnion } from "@inspector/core/json/rootUnion.js";
+import { declaresAnyFields } from "@inspector/core/json/rootUnion.js";
 
 /**
  * Returns the display label for an MCP entity that follows the BaseMetadata
@@ -17,19 +17,16 @@ export function resolveDisplayLabel(name: string, title?: string): string {
  * one place so the definition of "has fields" stays consistent if it ever
  * grows to consider `additionalProperties` etc.
  *
- * Root composition is resolved first, since a schema declaring its fields on a
- * root `allOf`/`oneOf`/`anyOf` has none of its own (#2123) — an App tool with
- * such a schema would otherwise launch with empty arguments rather than asking
- * for them.
+ * Root composition counts, since a schema declaring its fields on a root
+ * `allOf`/`oneOf`/`anyOf` has none of its own (#2123) — an App tool with such a
+ * schema would otherwise launch with empty arguments rather than asking for
+ * them. Counted from the composition members directly rather than from a
+ * resolved union, so a schema whose composition the form declines to flatten
+ * still reports the fields it has: it renders fewer controls, not none, and
+ * auto-invoking it would be wrong either way.
  */
 export function hasInputFields(tool: Tool): boolean {
-  const { base, branches } = resolveRootUnion(tool.inputSchema);
-  return (
-    Object.keys(base.properties ?? {}).length > 0 ||
-    branches.some(
-      (branch) => Object.keys(branch.schema.properties ?? {}).length > 0,
-    )
-  );
+  return declaresAnyFields(tool.inputSchema);
 }
 
 /**