What makes linear regression linear is that we assume that the output truly can be expressed as a linear combination of the input features.
This seems different from what I’ve known: linear regression is linear w.r.t the parameters instead of the inputs.
It is actually the case that linear regression makes the assumption that the output is a linear combination of the input features. This means that your model assumes no other transformations besides multiplication by a scalar and addition is done to any of the input features.
Of course, you can change what you mean by ‘input features’ and apply some other (non-linear) transformations to the features first, but strictly speaking that is not part of the linear regression. Saying that linear regression is linear w.r.t the parameters is just a short hand way of saying that only linear combinations of the inputs with the parameters as coefficients are allowed.