Heisenberg and Schrödinger pictures - clarification

Question related to The equivalence between Heisenberg and Schroedinger pictures.

I understand what’s explained in the link provided above. My textbook (Breuer and Petruccione’s Theory of Open Quantum Systems – but that’s similar to what’s done in the related Wiki page) does things a little differently, and I’m struggling to understand what’s going on.

What they say is:

Schrödinger picture and Heisenberg picture operators are related through the canonical transformation $A_H(t)=U^dagger(t,t_0)A(t)U(t,t_0)$, where we allow the Schrödinger picture operator $A(t)$ to depend explicitly on time.

They then derive the equation of motion as

$frac{d}{dt}A_H(t)=i[H_H(t),A_H(t)]+frac{partial A_H(t)}{partial t}$

where $H_H(t)$ is the Hamiltonian in the Heisenberg picture. Explicitely,

$frac{partial A_H(t)}{partial t}=U^dagger(t,t_0)frac{partial A(t)}{partial t}U(t,t_0)$

Now, what does it mean "we allow $A(t)$ to depend explicitly on time"? Isn’t the point of Schrödinger’s picture that operators do not depend on time, but states do? What does that "canonical transformation" mean? The operator $A$ on the RHS should not depend on time, how can we make it time-dependant and still be in Schrödinger’s picture? Shouldn’t the term $frac{partial A(t)}{partial t}$ always be $0$?