The main issue is that EV is often being read backwards.

EV is primarily a way to describe scene brightness or equivalent exposure settings, not “how bright the final photo looks.” A lower EV means dimmer light, so you need wider apertures, slower shutter speeds, or higher ISO to get a normal exposure.

For a given scene brightness, increasing ISO means you need less actual light at the sensor. So if ISO is included in the relationship, the ISO adjustment works opposite to aperture/shutter exposure time. In other words, higher ISO reduces the light required for the same final image brightness.

That’s why your intuition is basically correct: if a formula is written so that increasing ISO makes EV increase directly, it’s likely being rearranged or interpreted incorrectly. One of the community answers notes that the sign is effectively reversed in the version you quoted.

Also, EV does not mean “more exposed image” in the everyday sense. Two images made at different ISO settings can look equally bright even though the sensor received different amounts of light or used different sensitivity.