feat(ops): show relay apply progress on the replication card

Seconds_Behind_Source cannot answer "is it moving?". While the SQL thread
works through one large transaction the lag counter holds still — often at
0 — even though the replica is not caught up. The relay backlog does move,
and it comes out of the SHOW REPLICA STATUS the panel already runs, so this
costs no extra query and no connection to the source.

Adds applyProgress(), which reads Source_Log_File / Read_Source_Log_Pos vs
Relay_Source_Log_File / Exec_Source_Log_Pos and reports the fetched-but-not-
applied byte delta plus a percentage. Both positions are source binlog
coordinates, so they are only comparable while the two threads are on the
same file; across files the delta is meaningless (positions restart at ~4 in
each new file) and is reported as null rather than as a huge negative number.

The percentage deliberately stops at 99.99 while any backlog remains —
binlog positions are large enough that a real backlog of a few KB rounds to
100% and would render a lagging replica as caught up.

Not folded into `healthy`: a non-zero backlog is the normal state of a
working replica between fetch and apply, so alarming on it would cry wolf.

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

apps/web/src/lib/types.ts

@@ -99,10 +99,32 @@ export interface ReplicationStatus {
   lastIoError: string | null;
   lastSqlError: string | null;
   sourceHost: string | null;
+  apply: ApplyProgress | null;
   problem: string | null;
   checkedAt: string;
 }
 
+/**
+ * Relay-log apply progress, in source binlog bytes.
+ *
+ * Answers "is it moving?" when `secondsBehind` cannot: the lag counter sits
+ * still while the SQL thread works through one large transaction, but the
+ * backlog visibly shrinks. `backlogBytes === 0` is the only reading that means
+ * caught up — `percent` deliberately stops at 99.99 while bytes remain.
+ *
+ * Null fields when the two threads are on different source binlog files
+ * (`sameFile === false`), because the positions are then not comparable.
+ */
+export interface ApplyProgress {
+  sourceLogFile: string | null;
+  readPos: number;
+  relayLogFile: string | null;
+  execPos: number;
+  sameFile: boolean;
+  backlogBytes: number | null;
+  percent: number | null;
+}
+
 /** One of the four legacy Access files expected in the ingest folder. */
 export interface IngestFile {
   name: string;