I know that chess engine evaluations like +1.3 intuitively mean that White is evaluated to have an advantage equivalent to 1.3 pawns of material, or that -3.2 means that Black is evaluated to have an advantage equivalent to a little over a knight or bishop. But I am struggling to pin down what "having an advantage equivalent to" really means or how it could be implemented.
Such evaluations do not simply count the material on the board, but rather might translate into such an advantage in future. For example, an evaluation of -3.2 might be because Black, through optimal play, can force the capture of a white Bishop "for free" in the next couple of moves.
Other cases might not be so clearly linked to material advantage. For example, although currently level in material, Black, through optimal play, may gain a strong tactical advantage in future due to the white King being open.
My doubt here is that an engine will inevitably turn a -3.2 advantage into a future win for Black, even if the full path to checkmate is not clear. So the further we look into the future, the stronger the advantage will inevitably become for Black.
Hence my confusion. It seems that there is some "future looking" aspect to the evaluations, but depending on how far into the future we look, the evaluation for the current position changes.
Trying to "backwards-engineer" the concept, it seems that maybe there is a fixed window of turns somehow in which the advantage is considered, but this again seems material-based whereas an advantage might never translate into a material advantage in the short term. Perhaps another way would be to consider how much material must be given to the other side right now in order to make the position equal, but then there's the question of what material, and where to place that material.
Chess engines (not based on supervised learning at least) must implement this evaluation function in some way, and I guess that there is some standard definition in order to make the scores of different engines comparable (though I might be wrong).
My question is: is there a standard/typical, rigorous definition for these chess engine evaluations, and if so, what is that definition?