Add the profile page, and publish it as an embeddable panel

Developed in a separate session; committed here alongside the calendar work
that shares this repository's migration journal.

A person can now see their own Plex link, their Watch Now slots and their watch
history at /profile. The same panel is published in two further forms so that
accounts.sticknife.com on charon can carry it as one section of a wider
sticknife profile, next to the other services' sections.

  - watch_history (0024) records what has been played, keyed on the Plex
    history id so a re-sync cannot duplicate a row. Partial unique index,
    because that id is null for anything entered by hand.
  - plex_accounts.is_server_owner (0025) marks the one account whose viewing
    the server files under local account 1 rather than under its plex.tv id.
  - The embed carries its own layout, origin allowlist and a frame-height
    reporter, so the host page can size it without guessing.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

src/app/page.tsx

@@ -174,6 +174,8 @@ export default async function Home({ searchParams }: PageProps) {
   const kind = activeKind(resolvedSearchParams.tab);
   const query = singleParam(resolvedSearchParams.q)?.trim() ?? "";
   const collectionOnly = singleParam(resolvedSearchParams.collection) === "1";
+  // Set by the links on /profile, which point at a title rather than a tab.
+  const openExternalId = singleParam(resolvedSearchParams.open)?.trim() || null;
   // The same flag the admin layout and the server actions check, rather than
   // re-deriving it from the group list: a button that appears under one rule and
   // an action that refuses under another is the worst version of this.
@@ -211,6 +213,9 @@ export default async function Home({ searchParams }: PageProps) {
             </div>
           </div>
           <div className="flex flex-wrap items-center gap-2 text-sm">
+            <Link href="/profile" className="ampelos-ghost-button px-3 py-2 font-medium">
+              Profile
+            </Link>
             {isAdmin && (
               <Link href="/admin" className="ampelos-ghost-button px-3 py-2 font-medium">
                 Admin
@@ -274,6 +279,7 @@ export default async function Home({ searchParams }: PageProps) {
           watchNowItems={watchNowItems}
           slotCount={slotCount}
           isAdmin={isAdmin}
+          openExternalId={openExternalId}
         />
       </section>
     </main>