Question about definition of mobility in Drude model

Here, mobility is defined as |e| \tau / m, but e was already defined to be positive, so I feel like taking the absolute value is redundant. Is the mobility normally defined for any charge q, which could be positive or negative?

Furthermore, in the equation for \mathbf{v}, the absolute value of \mu is used. But if the absolute value of the charge is already taken in the definition of \mu, this absolute value doesn’t do anything, right?

you are completely right: the absolute value signs are redundant and only there to emphasize that it is a positive quantity