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.test.ts

@@ -118,6 +118,22 @@ describe("hasInputFields with root composition (#2123)", () => {
     ).toBe(true);
   });
 
+  it("sees fields on a union the form declines to flatten", () => {
+    // Otherwise an App tool with such a schema is treated as input-free and
+    // invoked immediately with `{}`.
+    expect(
+      hasInputFields(
+        tool({
+          type: "object",
+          anyOf: [
+            { type: "object", properties: { a: { type: "string" } } },
+            { $ref: "#/$defs/Other" },
+          ],
+        }),
+      ),
+    ).toBe(true);
+  });
+
   it("still reports no fields for a bare object schema", () => {
     expect(hasInputFields(tool({ type: "object" }))).toBe(false);
   });