But of course bisection doesn't just apply to curves, and bifurcation only refers to certain kinds of division. You wouldn't bifurcate a cake or a number, for example. I feel like it refers to a continuous process of splitting e.g. in time like a species that evolves into two species or in space like a road that forks into two roads.

I think the key difference is that bisect refers to slicing something into equally sized parts. This is sometimes the case (see eg. git bisect) but bifurcating the problem space would be the more general term.

While bisect is indeed slicing into two (mostly) equal parts, bifurcation is creating two branches, and in my mind, with the intent of following up on both (at least initially). So what's done here is bifurcation with pruning, and I think bisect would be a more appropriate term -- certainly the attempt should be made to divide the problem space into equal parts.