Reference host renders tool.name in the app header; base spec display precedence is title → annotations.title → name

Start in examples/basic-host/src/index.tsx at the tool-call header that renders toolCallInfo.tool.name, and compare the available title and annotations.title fields with the precedence described in schema/2025-11-25/schema.ts. Verify the header with a tool containing all three names; done means it displays the title-precedence value while preserving the existing server and tool header structure.

Describe the bug

The reference host renders the header above a rendered app from the raw tool
name, ignoring title and annotations.title. In
examples/basic-host/src/index.tsx
the tool-call header is:

<span className={styles.toolName}>{toolCallInfo.tool.name}</span>

with no fallback to either title field. Claude Desktop renders the same two
spans, server name then tool name, e.g. "Slidely list_design_systems" (also
observed on claude.ai), while the tool-call row in the same conversation shows
the tool's title. Screenshot attached shows both in one frame: "Checking
slides" in the task list, "Slidely get_presentation" on the card header.

The base spec defines the display precedence in
schema/2025-11-25/schema.ts:

• Tool.annotations: "Display name precedence order is: title,
  annotations.title, then name."
• BaseMetadata.title: "If not provided, the name should be used for display
  (except for Tool, where annotations.title should be given precedence over
  using name, if present)."
• BaseMetadata.name: "Intended for programmatic or logical use, but used as a
  display name in past specs or fallback (if title isn't present)."

The MCP Apps specification does not say how a host labels a rendered app, so
the reference host is the only guidance implementers have.

To Reproduce

1. Register a tool with a title, an annotations.title, and a
   _meta.ui.resourceUri pointing at a text/html;profile=mcp-app resource.
2. Call the tool from a host built on examples/basic-host, or from Claude Desktop.
3. Read the header rendered above the app.

Observed: the header shows the raw tool name, "Slidely list_design_systems".

Expected behavior

The header shows the tool's display name per the base spec's precedence:
"Listing design systems". The raw name could remain available in a tooltip or a
verbose view for provenance.

Logs

tools/list response (protocol 2025-11-25) for the request that produced the
rendered card, captured from the server log:

{
  "name": "list_design_systems",
  "title": "Listing design systems",
  "annotations": {
    "title": "Listing design systems",
    "readOnlyHint": false, "destructiveHint": false,
    "idempotentHint": true, "openWorldHint": false
  },
  "_meta": { "ui": { "resourceUri": "ui://slidely/chat-artifact-v4.html",
                     "visibility": ["model", "app"] } }
}

Rendered header DOM (Claude Desktop):

<span class="[unicode-bidi:plaintext]">Slidely</span>
<span class="text-muted [unicode-bidi:plaintext]"> list_design_systems</span>

Additional context

Related: anthropics/claude-code#37542 requested title in Claude Code's tool
rows and headers; closed as not planned.