Mourning doves
 

I found out why Pussy is spending so much time at that window. It
seems a pair of Mourning doves are often visiting outside. The doves
probably can't see inside because they don't fly off when she jumps up
there. I played a clip of Mourning dove call and she jumped up to the
window.

If I'm lucky the doves might build a nest there.

Mourning doves
 

My cats like those birds too :-)