Help me ID this bike: Bianchi Volpe?

Not definitive, but it all points to being one of the lugged Japanese Volpe years and has had a dropout conversion done to it.

The track ends aka dropouts look like they're for a bigger frame. That's why the seatstays are hitting at a weird angle. You wouldn't normally see that because frame manufacturers usually have different angle versions of their dropouts, or fixture things to hide it if not. It's not really a problem, it's probably fine. So the premise here is they're the track ends someone had available to use

The geometry doesn't look very track-ish. You could measure to get more clues but the tire clearance probably says enough. It's all a lot of inference, but why a bike with track ends would have everything else going on makes less sense.

Looking at the frame, its not a track silhouette. The rear wheel is further back, the BB is high for a track bike, and the short headtube is less-able to transmit power from the arms.

I suspect the bike started life as a 630mm wheel, or maybe even a 635mm. At this time it looks like common 622mm wheels, which is okay because tyre selection is larger. There's a lot of space between the fork's crown and the rubber, which implies the frame is approximately 90s at the newest and could be older (though the short headtube looks more modern)

All in all, if the conversions and changes were done in a workmanlike fashion, then the bike should be safe to ride. I'd suggest you get someone knowledgeable to have a close look at the bike, and give it a close once-over to make sure all is well. Once that's done, have fun on your new bike.

Nathan's answer is almost certainly correct and i'd like to expand it by pointing out that the Pista Classica has cheaper looking track ends than those brazed into your frame.

Your frame probably has some of the road features such as cable stops etc removed/filed off, part of the reason for the flat black paint.

At least it's still a Bianchi.

Further:

The Volpe should have cantilever brakes but yours must have had the bosses cut off and the not-quite ideal long reach calipers fitted.