Reuse upstream connections, and stop sniffing what we already know

Two costs sat in front of every video: a TLS handshake per upstream request,
and a round trip spent asking the proxy what kind of file it was about to
play.

The session cache was a thread-local, which never once hit -- the server
gives each connection a fresh thread, so every request found empty storage
and built a session, and with it a new connection to the CDN. Instrumented,
that was one session per request; a video is dozens of range requests and an
HLS stream one per segment. Sessions now live in a shared pool, checked out
for a request and returned when its response closes (for a streamed body,
after the last byte), so the connection stays warm. Measured against a
nearby CDN: 32-45ms per request becomes 9-11ms.

The player then HEADed the proxy before playback to sniff a content type --
and that HEAD ran a full upstream GET server-side, so two connections were
opened before the first byte of video was asked for. It now sniffs only when
neither the URL's extension nor yt-dlp's `protocol` says what the source is,
which is nearly never; `protocol` is newly carried through /api/resolve for
exactly this. A HEAD that does still happen asks upstream for one byte and
restates the 206 as a 200 describing the whole resource.

`format_note` joins the resolved fields too: the quality menu has been
reading it since 52d7802, but the backend was dropping it, so no note could
ever have been shown.

Tests (scratchpad, headless): sessions reused across requests, never shared
by two at once, returned after a client aborts mid-stream; HEAD probes one
byte while ranged and plain GETs are byte-identical; no HEAD for an mp4 or a
protocol-bearing URL, and one for a URL with neither.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01QBDkEXP4htyXTCZUwMLphd

frontend/js/feed.js

@@ -365,7 +365,7 @@ App.feed = App.feed || {};
         // What's actually on screen, so the quality menu can tick it.
         slide._activeUrl = resolved.url;
         const streamUrl = App.videos.buildStreamUrlFromSource(resolved);
-        const isHls = resolved.isLive ? true : /\.m3u8($|\?)/i.test(resolved.url);
+        const isHls = App.videos.classifySource(resolved).isHls;
 
         video.muted = state.feedMuted;
         video.preload = 'auto';