fix(web-presenter): dim-Markdown web fallback, memoize fetch conversion, strip note residue

Route a `web` result card's raw-content fallback through the TUI's dim
Markdown path (render() only recognized `card: 'generic'` as markdown
content, so web fallback rendered as bare undimmed text).

Memoize renderFetchOutput per (result, maxOutputChars) so the registry's
twin output.render / output.presentationMeta calls on the same frozen
result run one HTML->markdown conversion instead of two.

Remove the trailing `</content>`/`</invoke>` protocol residue from both
sides of the web-result-card Agent Note and re-record the pairing.

packages/web/tool-web/src/fetch.ts

@@ -266,6 +266,11 @@ interface RenderedFetch {
  * limits the source prefix processed synchronously, then applies again where the
  * complete output — header, rendered body, and footer — is known.
  *
+ * The tool registry calls this once through `output.render` and again through
+ * `output.presentationMeta`, both with the same frozen result value; the
+ * conversion is memoized per `(result, maxOutputChars)` so the synchronous DOM
+ * parse and turndown walk run once, not twice, on the same body.
+ *
  * @param result - the seam's fetch outcome.
  * @param maxOutputChars - cap on the complete returned string; a cut body gets
  *   the same fetch-something-narrower notice as provider-side truncation.
@@ -273,6 +278,32 @@ interface RenderedFetch {
  *   the provider, a source cut, or the cap trimmed the content.
  */
 export function renderFetchOutput(result: WebFetchResult, maxOutputChars: number): RenderedFetch {
+  const byCap = renderCache.get(result) ?? new Map<number, RenderedFetch>()
+  const cached = byCap.get(maxOutputChars)
+  if (cached !== undefined) return cached
+  const computed = computeFetchOutput(result, maxOutputChars)
+  byCap.set(maxOutputChars, computed)
+  renderCache.set(result, byCap)
+  return computed
+}
+
+/**
+ * Per-result memo for {@link renderFetchOutput}, keyed first on the frozen
+ * result value so a garbage-collected result drops its entry, then on the output
+ * cap (a deployment constant per registration). Collapses the registry's twin
+ * `render`/`presentationMeta` calls into one HTML→markdown conversion.
+ */
+const renderCache = new WeakMap<WebFetchResult, Map<number, RenderedFetch>>()
+
+/**
+ * The uncached conversion behind {@link renderFetchOutput}. Separated so the
+ * memo wraps exactly one call site and the conversion logic stays pure.
+ *
+ * @param result - the seam's fetch outcome.
+ * @param maxOutputChars - cap on the complete returned string.
+ * @returns the bounded text and effective truncation.
+ */
+function computeFetchOutput(result: WebFetchResult, maxOutputChars: number): RenderedFetch {
   const header = `Fetched ${result.url} (HTTP ${result.statusCode})\n\n`
   const rendered = renderBody(result.body, maxOutputChars)
   const prefix = `${header}${rendered.text}`

packages/web/tool-web/tests/tool-web.spec.ts

@@ -388,6 +388,27 @@ describe('web_fetch presentation meta and result view', () => {
     expect(formatFetchOutput(value, NO_CAP)).not.toContain('Content truncated')
   })
 
+  it('converts one HTML body once across the render and meta projections of the same result', () => {
+    // The registry calls output.render and output.presentationMeta with the same
+    // frozen result value; the memo must collapse them into one turndown walk so
+    // a large or deeply nested page is not parsed and converted twice. A second
+    // cap on the same result is a distinct entry, so it converts again.
+    const spy = vi.spyOn(TurndownService.prototype, 'turndown')
+    const value = {
+      url: 'https://a.test', statusCode: 200, truncated: false,
+      body: { kind: 'html' as const, content: '<p>hello</p>' },
+    }
+    try {
+      formatFetchOutput(value, NO_CAP)
+      fetchMetaFromValue(value, NO_CAP)
+      expect(spy).toHaveBeenCalledTimes(1)
+      formatFetchOutput(value, NO_CAP - 1)
+      expect(spy).toHaveBeenCalledTimes(2)
+    } finally {
+      spy.mockRestore()
+    }
+  })
+
   it('presents a completed fetch as a web/fetch card carrying the summary, titled by the url, without content', () => {
     const meta = fetchMetaFromValue({ url: 'https://a.test', statusCode: 200, truncated: false, body: { kind: 'text', content: '# Title' } }, NO_CAP)
     expect(presentFetchResult({ url: 'https://a.test' }, toolResult(meta, '# Title'))).toEqual({