Anchor game timer to first player join, not InitGame

An idle map load emits InitGame in games_sp.log without anyone joining,
which was falsely surfacing the game timer on empty servers. Track the
first `J;<guid>;<slot>;<name>` line inside each InitGame cycle instead
and back-compute the wall-clock start from that line's in-game MM:SS.
Removes the coarse client-side activeSince gate since the scanner is
now the source of truth.

src/lib/server/fleet/match-log.ts

@@ -12,10 +12,14 @@ import { resolveLogPath, tailLog } from './logs.js';
 export const MATCH_START = /InitGame:/;
 export const MATCH_END = /ExitLevel:\s*executed/;
 export const MATCH_SHUTDOWN = /ShutdownGame:/;
+// Player join line: `MM:SS J;<guid>;<slot>;<name>`. Every joining player emits
+// one — the first J; line after an InitGame is when the first player actually
+// entered the match, which is what "game time" should anchor to. An empty map
+// load still emits InitGame but no J; lines follow.
+export const MATCH_JOIN = /\sJ;[^;]*;\d+;/;
 // Every log line starts with a whitespace-padded MM:SS in-game time. Capture
-// it so we can back-compute a wall-clock game_started_at from the most recent
-// line — this stays accurate across process restarts and matches what the
-// game itself reports (e.g. `83:55 ExitLevel: executed`).
+// it so we can back-compute a wall-clock game_started_at that stays accurate
+// across restarts and matches what the game itself reports (e.g. `102:47 J;...`).
 const TIME_PREFIX = /^\s*(\d+):(\d{2})\s/;
 
 /**
@@ -57,12 +61,13 @@ export interface MatchScanResult {
 
 /**
  * Read the games_sp.log tail and classify the current match state:
- *   - `in-progress`: the most recent InitGame in the tail has no ShutdownGame
- *     or ExitLevel after it. Emits `startedAt` = now - MM:SS_of_last_line.
+ *   - `in-progress`: the most recent InitGame has at least one J; join line
+ *     after it and no ExitLevel/ShutdownGame after that. Emits `startedAt`
+ *     back-computed from the first join line's in-game MM:SS.
  *   - `ended`: the most recent InitGame is followed by ExitLevel/ShutdownGame,
  *     and the shutdown wasn't the trivial 0:00 idle cycle. Emits `endedAt` = now.
- *   - `idle`: the visible cycle was an idle map load (adjacent InitGame ->
- *     ShutdownGame at 0:00 with no ExitLevel between them). No timer.
+ *   - `idle`: no join line has fired inside the current InitGame cycle (empty
+ *     map loaded, or completed idle cycle at 0:00). No timer.
  *   - `no-signal`: log file missing / no InitGame anywhere in the tail —
  *     caller should leave persisted timer state alone.
  */
@@ -95,18 +100,30 @@ export async function scanMatchState(serverName: string): Promise<MatchScanResul
         return { kind: 'ended', endedAt: new Date().toISOString() };
     }
 
-    // In progress. Back-compute the wall-clock start from the most recent
-    // line's MM:SS prefix. Walk backwards from the tail to find the last line
-    // with a parseable time — falls back to the InitGame line itself (0:00).
-    let elapsedMs = 0;
-    for (let i = lines.length - 1; i > lastInit; i--) {
-        const t = parseTimePrefix(lines[i]);
-        if (t !== null) {
-            elapsedMs = t;
+    // In progress from InitGame's POV — but only anchor the game timer once a
+    // real player has joined. Find the FIRST J; line after lastInit.
+    let firstJoinIdx = -1;
+    for (let i = lastInit + 1; i < lines.length; i++) {
+        if (MATCH_JOIN.test(lines[i])) {
+            firstJoinIdx = i;
             break;
         }
     }
-    const startedAt = new Date(Date.now() - elapsedMs).toISOString();
+    if (firstJoinIdx === -1) return { kind: 'idle' };
+
+    // Back-compute the wall-clock start from the delta between the first join
+    // line's in-game time and the most recent parseable line's in-game time.
+    const joinGameTime = parseTimePrefix(lines[firstJoinIdx]) ?? 0;
+    let currentGameTime = joinGameTime;
+    for (let i = lines.length - 1; i > firstJoinIdx; i--) {
+        const t = parseTimePrefix(lines[i]);
+        if (t !== null) {
+            currentGameTime = t;
+            break;
+        }
+    }
+    const elapsedSinceJoin = Math.max(0, currentGameTime - joinGameTime);
+    const startedAt = new Date(Date.now() - elapsedSinceJoin).toISOString();
     return { kind: 'in-progress', startedAt };
 }