Its only possible to move one object at a time.
Select 2 objects and try to move them.
Its possible to move multiple blocks. But if one or more object is included it becomes unmoveable. Multiple blocks should be moveable regardless if an object is selected.
Android 13 Anytype 0.14.0-alpha
Its also not possible to move a block or blocks into an object by simple draging them on to it but maybe thats a topic for another thread.