fix: nostr-provider.js 404, DocsPage proxy-unaware URL, round-jump on late viewer join

Three more fixes found during live demo verification:

1. server/src/app.ts: the previous commit added <script src="/nostr-provider.js">
   to index.html and shipped the file into server/public/, but this app's
   static file serving is an explicit per-route allowlist, not a catch-all —
   there was no route registered for it, so it 404'd and the signer bridge
   silently never loaded. Added the missing app.get('/nostr-provider.js', ...)
   route.

2. DocsPage.vue: promptUrl (the displayed "give this URL to your AI" copy
   button) was built from window.location.origin — same root-cause bug class
   as the JoinBoutPage/BotProfilePage fix (ffd4dfd), just for a link instead
   of fetched content. Now resolves the real arena origin from the fetched
   prompt's own content (which IS correctly proxy-resolved server-side via
   arena-proxy) instead of the browser's current address.

3. FightPage.vue: opening a fight already in progress (e.g. a background
   poll-mode bot kept answering challenges while nobody had the viewer open)
   showed nothing until the next live round arrived — reads as "the fight
   jumped straight to round N". loadFight() always fetched the completed
   rounds (data.rounds) but nothing backfilled the visible log from them;
   only live SSE round_end events ever pushed into liveLogItems. Added
   backfillCompletedRounds(), called once on mount before wireSSE() connects,
   that renders a compact (non-animated — no scene/TTS replay) summary of
   every already-completed round and sets HP/round-counter to current state
   immediately.

4. BOTFIGHTS.md: documented the webhook_test signature exception (see ffd4dfd
   commit for the same fix already applied to the live doc endpoint's
   underlying example) — this file is frontend/public/docs/BOTFIGHTS.md,
   the static copy that predates today's /api/docs/prompt-only rendering
   fix; keeping both in sync since some flows may still reference the path.

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

frontend/src/pages/FightPage.vue

@@ -193,6 +193,52 @@ async function initLiveScene() {
   scrollLiveLog()
 }
 
+// Backfill already-completed rounds when opening a fight already in progress
+// (e.g. a background poll-mode bot kept fighting while nobody had the viewer
+// open — the log otherwise starts empty and the NEXT live round is the first
+// thing to ever appear, reading as "the fight jumped straight to round N").
+// Deliberately NOT calling handleRoundEnd() for these — that triggers full
+// scene animation/TTS/fanfare per round, which would replay every missed
+// round in real time before the viewer could show anything current. This is
+// a compact, non-animated log backfill only; HP/round-counter state is set
+// directly from the fetched fight's current values.
+function backfillCompletedRounds() {
+  const fd = liveFightData.value
+  const roundsData = (fd as any)?.rounds as Array<Record<string, any>> | undefined
+  if (!fd || !fd.botA || !fd.botB || !roundsData?.length) return
+
+  for (const r of roundsData) {
+    const round = r.roundNumber
+    const aWon = r.winnerId === fd.botA.id
+    const bWon = r.winnerId === fd.botB.id
+    const winnerName = aWon ? fd.botA.name : bWon ? fd.botB.name : 'DRAW'
+    liveLogItems.value.push(
+      { type: 'header', round, text: `ROUND ${round}: ${challengeLabel(r.challengeType)}`, color: 'neon-purple' },
+    )
+    if (r.botAResponse) {
+      liveLogItems.value.push({ type: 'responseA', round, text: `${fd.botA.name}: ${r.botAResponse}`, color: 'neon-cyan' })
+    }
+    if (r.botBResponse) {
+      liveLogItems.value.push({ type: 'responseB', round, text: `${fd.botB.name}: ${r.botBResponse}`, color: 'neon-pink' })
+    }
+    if (r.narration) {
+      liveLogItems.value.push({ type: 'narration', round, text: `>> ${r.narration}`, color: 'neon-yellow' })
+    }
+    liveLogItems.value.push(
+      { type: 'result', round, text: `${winnerName} ${aWon || bWon ? 'wins round!' : '- no winner'} (${r.botAScore ?? 0} vs ${r.botBScore ?? 0})`, color: aWon ? 'neon-cyan' : bWon ? 'neon-pink' : 'text-muted' },
+      { type: 'divider', round, text: '', color: '' },
+    )
+  }
+
+  // Reflect current state immediately — don't wait for the next live round
+  // to update HP/round counter away from their initial defaults.
+  const lastRound = roundsData[roundsData.length - 1]
+  liveCurrentRound.value = lastRound.roundNumber
+  if (typeof (fd as any).botAHp === 'number') liveHpA.value = Math.round(((fd as any).botAHp / 200) * 100)
+  if (typeof (fd as any).botBHp === 'number') liveHpB.value = Math.round(((fd as any).botBHp / 200) * 100)
+  scrollLiveLog()
+}
+
 // --- SSE event wiring ---
 // Track in-progress round animation so fight_end can wait for it
 let _roundEndPromise: Promise<void> | null = null
@@ -527,6 +573,10 @@ onMounted(async () => {
   }
 
   if (isLive.value) {
+    // Show any rounds that already happened before this viewer connected
+    // (see backfillCompletedRounds() for why — a background bot doesn't wait
+    // for a spectator) before wiring the live SSE stream for what's next.
+    if (!isHumanFight.value) backfillCompletedRounds()
     startPolling({ onFinished: () => stopHumanPolling(), onTimeout: () => stopHumanPolling(), keepLive: isHumanFight.value })
     wireSSE()
     // Scene init + human polling are handled by the liveFightData watcher