Quiet the logs and capture the errors that were missing

- Activity page: "Delete all" empties the open tab (api/admin/logs/clear-logs,
  super admin only, logged under system)
- Stop logging every WebSocket connect
- Log unexpected API errors (safeErrorMessage -> logUnexpectedError), every
  failed bot job attempt and every job the queue lost
- Drop the cron jobs' console output; a failed model sync goes to the logs

Co-Authored-By: Claude Opus 5.5 <[email protected]>

src/schemas/log-schema.ts

@@ -0,0 +1,17 @@
+import { z } from "zod";
+import { LogCategories } from "@/src/dict/log-categories";
+
+const LogCategoryValues = LogCategories.map((lc) => lc.value) as [
+    (typeof LogCategories)[number]["value"],
+    ...(typeof LogCategories)[number]["value"][],
+];
+
+/**
+ * `POST api/admin/logs/clear-logs`: deletes every log in one category, or
+ * every log when it is left out (the "All" tab).
+ */
+export const ClearLogsRequestSchema = z.object({
+    category: z.enum(LogCategoryValues).optional(),
+});
+
+export type ClearLogsRequest = z.infer<typeof ClearLogsRequestSchema>;