Some pedestrian crossing buttons play different audible beats so blind people know when they can cross. Famously the beat of one in Sydney was sampled for a Billie Eilish song (https://www.youtube.com/watch?v=I-zeJRjP6xA skip to around 4:00 mins).

However others have no indicator or sound. To make things even more confusing is the pedestrian crossings can also be programmed to happen automatically at peak times with no button press, but absolutely need a button press outside of peak hour.

No, no indicators. Just a great big shiny button to press (or not press if you are my wife).

In Finland there is just a light above button in the box. It will light up when it is activated. Or actually when cycle is activated so also for other side. Decent enough UI for non blind, with blind I think there is sound in some cases.