Since the official osu! client does not run natively on ChromeOS without technical workarounds like Linux mode, web ports are the most common "unblocked" solution: Web osu!mania (timhortonsyo)

Rhythm games require precise timing. Lag or audio delays can ruin your combos. Follow these steps to optimize ChromeOS:

The most straightforward way to get your rhythm fix on a school Chromebook is to use a web-based version of the game. These are browser-based adaptations that let you play osu!mania beatmaps without needing to download or install any software.