The problem was (in my case) that I didn't realize Time.deltaTime can get in the way in some cases. Explained by @DMGregory and @Kevin in the comments.

Sounds like you're double-dipping by multiplying by Time.deltaTime then. A mouse delta will already be larger on a long frame or smaller on a short frame, given a constant speed of mouse movement, just given that there's more or less time to accumulate travel. By multiplying by deltaTime, you're effectively squaring your frame time adjustment, making it more sluggish at high framerates.

So using Time.deltaTime in Unity's new input system is not necessary. Also, I've learned yet again that you can't always trust tutorials! As the bugged code came from a tutorial.

The problem was (in my case) that I didn't realize Time.deltaTime can get in the way in some cases. Explained by @DMGregory and @Kevin in the comments.

Sounds like you're double-dipping by multiplying by Time.deltaTime then. A mouse delta will already be larger on a long frame or smaller on a short frame, given a constant speed of mouse movement, just given that there's more or less time to accumulate travel. By multiplying by deltaTime, you're effectively squaring your frame time adjustment, making it more sluggish at high framerates.