Many languages have generic, ambiguous umbrella terms, it's the sloppiness of the spec picking one.
Interestingly enough, I can confirm as a native speaker of one such language (🇸🇮Slovene), that outside of discrete mathematics and tech, the words are often used interchangeably. This suggest that the lack of a word in English isn't the cause but the effect. The distinction was likely not necessary before the modern era, so old (==all) languages never created/adopted proper terminology.
That covers a lot of ground, by design. But a 'number' it isn't.
Though 'quantity' as described in another post still sounds the best given the sub 1 and add 1 buttons.
I think it's just an evolution of our education, preferred input devices, and specs all catching up with each other. On a desktop I just start typing numbers from the keyboard. On a smartphone I click on a credit card field, if the field expects "text" I have to click "123" then input the number using a number row with smaller target sizes. I would greatly prefer to directly show me a number pad.
Point being, blaming the language used for writing the spec, when you readily offered up a better alternative, feels misguided to me.
It's an unfortunate accident of the English language that both are commonly called ‘numbers’. We might not have had this confusion if some other language were the lingua franca of computing.