Custom buttons won't fire "input" event

I am building a calculator and I want to allow the user to also type it using their own keyboard, for that, I am trying to use "input" event on the input-text, so it fires on both ways of typing.

The thing is that the input event isn't firing when clicking on the DOM buttons, only when I use my keyboard. Why?

Codepen: https://codepen.io/leoncelestino/pen/NWZwYgq (Use mobile view for better UI)
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