explicitly fall back to the connection's database and schema when constructing the stage FQN

Author: sfc-gh-svishnu

src/snowflake/cli/_plugins/streamlit/streamlit_entity.py

@@ -260,8 +260,16 @@ def _deploy_legacy(
             if isinstance(self.model.identifier, Identifier)
             else self.model.identifier or self.entity_id
         )
+        # Get the fully qualified stage name, falling back to connection database/schema
+        stage_fqn = FQN.from_string(self.model.stage)
+        db_to_use = stage_fqn.database or self._conn.database
+        schema_to_use = stage_fqn.schema or self._conn.schema
+        if db_to_use:
+            stage_fqn = stage_fqn.set_database(db_to_use)
+        if schema_to_use:
+            stage_fqn = stage_fqn.set_schema(schema_to_use)
         stage_root = StageManager.get_standard_stage_prefix(
-            f"{FQN.from_string(self.model.stage).using_connection(self._conn)}/{name}"
+            f"{stage_fqn.identifier}/{name}"
         )
         sync_deploy_root_with_stage(
             console=self._workspace_ctx.console,