You make an observation. Then the wavefunction continues, but you have a constraint, a point of data. Has the quantum system become classical? No. What has happened is a correlation has spread, a particular case of a larger phase space has been chosen.
Chiribella's Purification Principle seems a good way of conceptualising what an observer is. This helps us understand how the thermodynamic arrow of time & movement through phase can be different but point in the same direction, as per say Loop Quantum Gravity (information spreads out forwards in time, because when it concentrates that would be literally a movement backwards in time, erasing records). It's crucial to think hard about what information is. It's also very important to understand how big phase space is even for simple-seeming systems.
The uncertainty principle 'hides' a certain amount of information, a precise measurement with an observation, maximises the uncertainty in a canonically conjugate variable. From there, uncertainty can grow again until another observation, until information about the quantum subsystem leaks out, constraining the phase space again.
So the appropriate picture is not a wavefunction collapsing once and for all, but rippling uncertainties. This is captured by the metaphor of Indra's Net. Instead of a fixed external unified reality being updated by events, instead there is information rippling around, reflecting through pictures, subjectivities, which have given constraints, given data points, about all the other subjectivities (see this discussion on relating subjectivity to physics Is the idea of a causal chain physical (or even scientific)?).
Deutsch & Marletto's Umiversal Constructor Theory helps us to understand that 'things', systems, aren't fixed outputs, defined states, but sets of possibilities. They have a topological existence, within the limits of relevant uncertainties, in which the 'truth' of a particular iteration is literally non-existent, the system isn't the 'reduced' uncertainty particular, but exists as a set of counterfactuals as viewed from after taking an observation. Before the observation the shape in phase space is what is real, the topology of the different possible outcomes.