Learn English – Neither nor inversion

"So beautiful was day we could not sit at home." is not the inversion, and is not grammatically correct. Try "So beautiful was it THAT we could not sit at home." This is still unnatural, but is a faithful inversion of "It was so beautiful that we couldn't stay home." Although you might think "day" is implied in the original non-inverted sentence, it is not stated. (I might think "weather" was implied, but I would not insert that into the inverted sentence either!)

As for "Such was a beautiful day we could not sit at home.", this is also not grammatical, and not the proper inversion. What you need is : "Such a beautiful day was it that we could not sit at home". Again, not natural, but properly inverted.

The "such a big house" one is correctly inverted. Very unnatural, but correctly inverted.

The next one could be inverted thus: "Their excitement was such that they began to jump up and down".

So, sentences with either kind of "such" can be inverted, even though some such inversions might sound unnatural.

If what the reporter meant by only yesterday was indeed a negative—"not before yesterday"—inversion would as you say be in order.

In this case, however, the phrase means "as recently as yesterday"; it might be paraphrased "just yesterday". It is consequently not apprehended as a negative, and does not call for inversion.