[TASK-395688] Perfect Meetings: better people research, confidence, and profiles (#122)

## Summary
The meeting researcher missed an attendee because the prompt replaced
the email-derived name with "(full name unknown)". The agent then
searched only the address and gave up after one search.

- **Research prompt:** passes the email handle as a hint (`email handle
"demarcus"`) and the likely company name, and tells the agent which
searches to try, in order, when the full name is unknown (handle +
company + LinkedIn, handle + company, then the quoted email). It must
run at least two before giving up.
- **Confidence:** new People `Confidence` select (High/Low). A partial
match (such as a first name at the right company) is saved as Low. A
later match can replace it, but it never overrides High. Setting High by
hand locks the name and role. The Next meeting card shows `(low
confidence) <role>`.
- **People profiles:** each prep writes a `## Profile` section above `##
Notes` on every attendee's page:
  - role and responsibilities, with the source linked
- meetings in the last 90 days from the calendar (three one-month
`listEvents` calls), linked to Meetings pages
  - a summary of recent meetings and email

A Low match gets a warning callout. Profile writes are best effort and
never fail the brief.
- **Profile links:** new People `LinkedIn`, `X`, `Instagram` and
`Personal site` URL properties. The researcher looks only for the empty
ones, and the prompt lists known profiles so it skips them. Each URL has
to be on its network's domain. The Next meeting person cards link to the
profiles that are set.
- **Parsing:** unwraps Markdown links the agent added around emails,
domains, and URLs. It had returned `[mintlify.com](http://mintlify.com)`
as a domain.

## Testing
- `npm run check`, `npm test` (89 passing), `npm run build`
- Deployed to dev and tested with hand-made test meetings, so no
calendar invites were created or sent:

🤖 Generated with [Claude Code](https://claude.com/claude-code)

---------

Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

Author: neilsarkar

apps/templates/perfect-meetings/APP.md

@@ -21,7 +21,19 @@ meeting objective.
 
 Open a meeting to review its **Meeting prep** and take notes under **Notes**.
 Refreshing the prep leaves your notes untouched. Tick **Regenerate prep** to
-request a fresh brief or retry a failed one.
+request a fresh brief or retry a failed one. Each person's **Confidence** shows how
+sure the researcher is of their name and role. Low means it matched only part
+of the name, such as a first name at the right company; their card shows
+"(low confidence)", and a later brief may correct them. Set it to High once
+you have checked a person to keep their name and role.
+
+Each brief also updates a **Profile** at the top of each attendee's page in
+**People**: their role and responsibilities, meetings with them in the last 90
+days, and a summary of recent meetings and email. Write your own notes under
+**Notes** on that page; refreshes leave them untouched. The researcher also
+fills in their **LinkedIn**, **X**, **Instagram**, and **Personal site** when
+it finds them, and the meeting card links to them. It only looks for profiles
+that are empty, so correct a wrong one by replacing it.
 
 Meetings update when calendar events change, with an hourly catch-up, and
 every catch-up is logged in **Workflow runs**. Briefs are prepared for new
@@ -32,7 +44,7 @@ with only coworkers do not appear by default.
 
 <details>
 <summary>App data</summary>
-	<mention-page url="{{people-db}}">People</mention-page> — Look up outside attendees and their roles.
+	<mention-page url="{{people-db}}">People</mention-page> — Look up outside attendees, their roles, and their profiles.
 	<mention-page url="{{companies-db}}">Companies</mention-page> — Browse company summaries and websites.
 	<mention-page url="{{meetings-db}}">Meetings</mention-page> — Switch to **Calendar** or **All meetings** to browse dates and past notes.
 	<mention-page url="{{sync-runs-db}}">Workflow runs</mention-page> — Every calendar catch-up, with its status and any error.

apps/templates/perfect-meetings/blocks/nextMeeting/index.html

@@ -1,2 +1,12 @@
 <!doctype html>
-<html lang="en"><head><meta charset="UTF-8" /><meta name="viewport" content="width=device-width, initial-scale=1.0" /><title>Next meeting</title></head><body><div id="root"></div><script type="module" src="/index.tsx"></script></body></html>
+<html lang="en">
+  <head>
+    <meta charset="UTF-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>Next meeting</title>
+  </head>
+  <body>
+    <div id="root"></div>
+    <script type="module" src="/index.tsx"></script>
+  </body>
+</html>