へと is used when you are directing your audience's attention to the content that comes after the と for emphasis. 「やや強意の副詞的表現に属することを表す」
The white ball disappeared into the crystal clear blue sky
透き通るような青空の中 へ 白いボールが吸い込まれていく
Without the と it is simply a statement of fact.
Q: "What did the ball disappear into?"
A: "The blue sky."
But with the と, the "crystal clear blue sky" is emphasized in the mind of your audience.
Of course this means that the same sentence without the と would be grammatically correct, be understood by native speakers, and most likely not be thought of as unnatural or needing correction of any sort. The difference is in the imagery you paint in the mind of your audience along with the associated feelings.
Of the examples in the question I think this is easiest to see with
～へと先送りされる : to be postponed to ~
If we say
7月15日へ先送りされる。 Then something has been postponed until July 15. A simple statement of fact.
But if we say
7月15日へと先送りされる。Then something has been postponed until July 15 and we are letting our audience know that we feel this is far away and is going to be a long wait.
Which leads to another usage of へと. By breaking the flow of the sentence with と, you indicate that the content that comes next did not happen easily or without effort.
This is probably easiest to see with
～へと旅立つ : to make a trip to ~
If we say
北海道へ旅立つ。 Then all we are saying is that we made a trip to Hokkaido.
But if we say
北海道へと旅立つ。 Then we imply a journey that required effort and the imagery painted for the audience takes on a whole new depth.
へと seems to be equivalent to へ or even に.
It is, in terms of meaning, but as you can see above the feeling can be quite different.
How is へと different from へ?
The difference is in the emphasis that と brings to the sentence.
How is へと different from に?
There are many cases where へ and に are the same. The 広辞苑 dictionary uses に in definition 2 of the particle へ. So since the と is adding emphasis, the answer to this question lies in the difference between へ and に, which is beyond the scope of this Q&A. On a side note though, に and と also have such a relationship. (～となる and ～になる)
What does と do and what nuance does it add?
I hope the above answer has made that clear by now. (^_^)