Quantum fields are indeed operator-valued, but their interpretation in terms of particle types is based on the concept of excitations or quanta of those fields. Let me explain further.
In quantum field theory, fields are operators that create and annihilate particles. These operators act on a vacuum state to produce particle states. The different types of particles correspond to different excitations of the underlying quantum field. For example, the electromagnetic field corresponds to the creation and annihilation of photons, which are the quanta of the electromagnetic field.
The reason why we associate particle types with quantum fields rather than operator types is that the quantum field itself contains information about the dynamics and symmetries of the corresponding particles. The properties and behavior of particles, such as their mass, charge, and interactions, are encoded in the mathematical structure of the quantum field. By studying the properties of the field, we can understand and describe the particles that arise from it.
In a sense, the quantum field acts as a mediator between the mathematical operators and the physical particles. The operators describe the fundamental degrees of freedom of the field, but it is the field itself that gives rise to the particles we observe in experiments. The field's excitations, or quanta, are what we identify as individual particles.
So, while the quantum fields are operator-valued, the association with particle types comes from the interpretation of the excitations of those fields as the particles themselves. The field operators provide a mathematical framework for describing the creation and annihilation of particles, and the properties of the particles are encoded in the dynamics of the fields.