Need mfgr of double hung casements w/“PG” engraved on lock

The standard approach to sealing the top of the lower sash raised for the AC is a foam strip placed between the outward facing uper edge of the inner sash and the outer glass pane.

This gap is on the inside of the house.

The birds you mention must be getting in through the lower gap between the lower rail of the upper sash and the glass pane on the inside sash. There is no reason you could not use the same type of foam insulator on the outside (assuming you can safely reach the window). While this is not a hard barrier that will prevent a forceful assault by a determined attack bird, it probably will be enough to discourage the accidental intruder.

The foam will likely deteriorate much more quickly outdoors, but should last a season.

These windows must have been installed into window casements that were built in place or reused from previous windows. The reason I comment about that is that if the windows were new units with the windows themselves pre-hung in the casements it is hard to believe that they would have the misfit that you describe as delivered from the factory.

In any case you would do well to see if you can talk one or two other contractors to come out to look at the installation to see what feedback they would give to you.

Sounds to me like you need to argue the case for a replacement set of new windows. If by chance you have not paid for the job you should withhold such payment until the problem is corrected to your satisfaction. If you have already paid then you have lost a certain amount of leverage but threat of a civil suit may be in order if you do not get a suitable response from the contractor. Of course you have to weigh the cost of getting involved in litigation against the size of investment already made in the windows.