In many rhythm games (like step mania, Osu! mania, etc.), the inputs are arrow shaped. Where does this "standard" of rythm/music games come from ?
I can't speak for Osu!mania directly, but Stepmania was based on Dance Dance Revolution (DDR), which had a pad below the player with the 4 directional arrows, which the player had to step on in time with the music. Stepmania was meant to be an open sourced clone of DDR, so many of it's original mechanics and design would come from the DDR franchise mechanics.
The "step" in stepmania is a reference to how Dance Dance Revolution (and clones like Stepmania) are supposed to be played. By stepping on the corresponding arrows at the right time to the beat.
As far as I'm aware, with Osu!mania there are just some maps which have this arrow layout. Wikipedia's page on Osu!mania says:
osu!mania is a game mode which consists of a piano-like style of clicking notes to the beat, similar to the Beatmania IIDX series. The number of keys ranges from 1 to 9, with 4 keys and 7 keys being more popular among players.
So Osu!mania is more of a direct clone of the Beatmania series, which doesn't use the dance pads like DDR was designed for. I assume that some Osu!mania tracks that only have 4 keys (which it says is a popular format) often map those keys to arrows, so that it resembles the traditional beat games like DDR and Stepmania.
As far as I can tell, the standard of using 4 arrow keys to represent the inputs is because Stepmania is directly based off Dance Dance revolution, and because 4-key Osu!mania levels sometimes pay homage to DDR and Stepmania, as the gameplay is similar.