fix(ai-vault): require node:sqlite backup support in remote SQLite probes (#24086)

* fix(ai-vault): require the full SyncDatabase node:sqlite surface in host SQLite probes

The SSH and WSL OpenCode probes admitted any Node with DatabaseSync, so
Node 22.13-22.15 hosts (no backup export) skipped the pinned-runtime
fallback. Share one admission predicate with isSqliteAvailable() and
embed its source in both probe scripts.

* build(cli): list the node:sqlite admission predicate in the CLI project

---------

Co-authored-by: m4air <m4air@m4airs-Air.localdomain>

src/main/sqlite/node-sqlite-reader-api.ts

@@ -0,0 +1,20 @@
+/**
+ * Source of the node:sqlite admission check, embedded in remote/WSL probe scripts so a
+ * host's Node passes exactly when `isSqliteAvailable()` would admit it there.
+ * Why `backup`: it landed with the DatabaseSync options SyncDatabase relies on (Node 22.16),
+ * so Node 22.13–22.15 must take the pinned-runtime fallback.
+ */
+export const NODE_SQLITE_READER_API_SOURCE =
+  "(m)=>typeof m==='object'&&m!==null&&typeof m.DatabaseSync==='function'&&typeof m.backup==='function'"
+
+/** In-process twin of {@link NODE_SQLITE_READER_API_SOURCE}; a parity test keeps them equal. */
+export function hasNodeSqliteReaderApi(sqlite: unknown): boolean {
+  return (
+    typeof sqlite === 'object' &&
+    sqlite !== null &&
+    'DatabaseSync' in sqlite &&
+    typeof sqlite.DatabaseSync === 'function' &&
+    'backup' in sqlite &&
+    typeof sqlite.backup === 'function'
+  )
+}