fix(setup): name client configuration syntax from one reader table (#10586)

* fix(setup): name client configuration syntax from one reader table

Each client format now maps to one reader description (syntax, strict or
JSONC, BOM and empty-file handling, strict-JSON repair). The document
parser, the strict-JSON rewrite decision and uninstall's diagnostic all
read it, so uninstall no longer re-derives a syntax name that called
Goose's YAML and JSONC-admitting clients "JSON".

* test(hopper): retry cleanup after confirmed application exit

src/application/ClientConfigurationDocument.shape.test.ts

@@ -2,6 +2,7 @@ import { describe, expect, it } from "vitest";
 
 import {
   ClientConfigurationShapeError,
+  clientConfigurationSyntaxName,
   parseClientConfiguration,
   shadowedClientServers,
 } from "./ClientConfigurationDocument.js";
@@ -27,6 +28,44 @@ describe("parseClientConfiguration shape diagnostics", () => {
     expect(error.message).toContain("object");
   });
 
+  // The diagnostic syntax name must describe what the reader actually admits.
+  it.each([
+    ["json", "JSONC"],
+    ["vscode", "JSONC"],
+    ["opencode", "JSONC"],
+    ["kilo", "JSONC"],
+    ["zed", "JSONC"],
+    ["amp", "JSONC"],
+    ["copilot_cli", "JSONC"],
+    ["fx", "JSONC"],
+    ["claude_code", "JSON"],
+    ["pi", "JSON"],
+    ["kimi", "JSON"],
+    ["lm_studio", "JSON"],
+    ["zcode", "JSON"],
+    ["toml", "TOML"],
+    ["grok", "TOML"],
+    ["goose", "YAML"],
+    ["hermes", "YAML"],
+  ] as const)("names %s configuration syntax %s", (format, name) => {
+    expect(clientConfigurationSyntaxName(format)).toBe(name);
+    const accepts = (text: string): boolean => {
+      try {
+        parseClientConfiguration(text, format);
+        return true;
+      } catch {
+        return false;
+      }
+    };
+    if (name === "TOML") expect(accepts("keep = 1\n")).toBe(true);
+    if (name === "YAML") expect(accepts("keep: 1\n")).toBe(true);
+    if (name === "JSON" || name === "JSONC") {
+      expect(accepts('{"keep":1}')).toBe(true);
+      expect(accepts('{"keep":1,}')).toBe(name === "JSONC");
+      expect(accepts('{"keep":1 /* comment */}')).toBe(name === "JSONC");
+    }
+  });
+
   it("still rejects unparsable JSON with SyntaxError", () => {
     expect(() => parseClientConfiguration("not-json", "json")).toThrow(
       SyntaxError,