I have no idea what your point is.however, in the context of the problem, "the mass's acceleration" refers to the conditions of the already postulated forces; not to some other unspecified source of tangential acceleration − I agree that it arguably was remiss of the testers to not say anything about how an orbit would be incipiated to begin with.
The given solution claimed that when the velocity is vertical there is no vertical acceleration, it relied on this for completing the solution, yet it offered no reasoning to arrive at the claim. Yes, it can be shown to be true in the particular context of the problem, but that is a nontrivial step and is conspicuously absent from the given solution.
This has nothing to do with hypothesising other forces nor how the motion was initiated.
You are again confusing how to solve the original physics problem with whether the official solution is valid. If the official solution had first established that the motion is uniform, or if it had been given as a fact in the problem statement, I would have no complaint with those two sentences.You had stated that only with the uniform circular motion would the argument in the first two sentences of the solution be correct ##-## given that on the way down, ##mg## is added, while on the way up, it is subtracted, the question whether the interaction of the spring force with the gravitational force keeps the velocity constant seems germane to me.