hilbert space - An apparent contradiction with basis transformation in quantum mechanics

Under a change of basis i.e., transforming from one orthonormal $\{|\phi_n\rangle\}$ base to another $\{|\phi^\prime_n\rangle\}$ (when looked from a passive point of view) implies that the state doesn't change but only the "components" change: $$|\psi\rangle=\sum\limits_{n}\langle\phi_n|\psi\rangle|\phi_n\rangle=\sum\limits_{n}\langle\phi^\prime_n|\psi\rangle|\phi^\prime_n\rangle$$ where $|\phi^\prime_n\rangle=U|\phi_n\rangle$, $U$ being an unitary operator which ensures the ortonormality of two bases. Using $$\langle\phi_n|\psi\rangle\to\langle\phi^\prime_n|\psi\rangle=\langle\phi_n|U^{-1}|\psi\rangle\tag{A}$$ one can also say that "net result'' of a basis transformation as an active transformation where the base is left unchanged but any state $|\psi\rangle$ changes to $U^{-1}|\psi\rangle$. In two different bases, an operator $A$ can be expanded as: $$A=\sum\limits_{m}\sum\limits_{n}|\phi_m\rangle\langle\phi_m|A|\phi_n\rangle\langle\phi_n|=\sum\limits_{m}\sum\limits_{n}|\phi^\prime_m\rangle\langle\phi^\prime_m|A|\phi^\prime_n\rangle\langle\phi^\prime_n|.$$ Using $$\langle\phi_m|A|\phi_n\rangle\to\langle\phi^\prime_m|A|\phi^\prime_n\rangle=\langle\phi_m|U^{-1}AU|\phi_n\rangle.\tag{1}$$ Hence, the result of the basis transformation, is an active transformation where the operator changes as $A\to U^{-1}AU$ but the base is left unchanged.

What happens to the various object under basis transformation? It is easy to see that for any $|\phi\rangle,|\psi\rangle$ in the Hilbert space, the inner products remain unchanged: $$\langle\psi|\phi\rangle\to \langle\psi| UU^{-1}\phi\rangle=\langle\psi|\phi\rangle.$$ Also $$\langle\psi|A|\phi\rangle\to \langle\psi|U(U^{-1}AU)|U^{-1}\phi\rangle=\langle\psi|A|\phi\rangle\tag{2}$$ i.e., objects such as $\langle\psi|A|\phi\rangle$ do not chnage.

Doesn't Eq.(2) contradict Eq.(1)? Eq.(2) says objects such as $\langle\psi|A|\phi\rangle$ do not change. But Eq.(1) says matrix elements of an operator changes under basis transformation. But Eq.(1) is just a special case of Eq.(2). What is wrong here with my understanding?

Note: I'm trying to compare active transformation with passive transformation. Either the basis changes or the system changes. Note that Eq.(A) and Eq.(1) says if the base is assumed to be fixed, then both the state and the operator must change. I'm reading this from Modern Quantum Mechanics by Sakurai, section 1.5