Certainly this has a backup in the sunnah:
When the Messenger of Allah (ﷺ) stood to offer a voluntary prayer he would say: " Allahu Akbar Wajahtu wajhi lilladhi fataras-samawatiwal-arda hanifan musliman wa ma ana minal-mushrikin. Inna salati wa nusuki wa mahyaya wa mamati lillahi rabbil-alamin, la sharika lahu, wa bidhalika umirtu wa ana awwalul-muslimin. Allahumma antal-maliku la ilaha illa anta subhanaka wa bihamdik (Allah is Most Great. Verily, I have turned my face toward Him who created the Heavens and the Earth hanifa (worhsipping none but Allah Alone), as a Muslim, and I am not of the idolaters. Verily, my Salah, my sacrifice, my living, and my dying are for Allah, the Lord of the all that exists. He has no partner. And of this I have been commanded, and I am the first of the Muslims. O Allah, You are the Sovereign and there is none worthy of worship but You, glory and praise be to You.)" Then he would recite. (See for example Sunan an-Nasa-i, Sunan abi Dawod and Jami' at-Tirmidhi)
It is called du'a al-Istiftah -in Arabic--the supplication at the beginning of the prayer (I don't know in which language it is called Sana), there are other wordings too which are preferred by other schools of jurisprudence. The Maliki school of fiqh doesn't consider du'a al-Istiftah at all all.
One of them is referred to in your link (as Sana):
'Subhanakallahumma, wa bihamdika tabarakasmuka wa ta'ala jadduka wa la ilaha ghairuk (Glory and praise be to You, O Allah. Blessed be Your name and exalted be Your majesty, there is none worthy of worship except You. (See for example in Sunan an-Nasa-i, Jami' at-Tirmidhi, Sunan abi Dawod and Sunan ibn Majah)
A third wording can be found in this hadith.
The link also provides what a person should utter if he would utter the niyyah. Note that there's no proof that niyyah needs to be done verbally: Can niyat (intention) be done by heart, or must it be declared verbally?.
Many Muslims before starting the prayer recite du'a's to help themselves to concentrate on the prayer the wording from the first du'a can be one of them as it is used in other occasions too as here when turning the sacrificed animal towards the qiblah.
Basically you seem to have got confused based on that link as they posted this du'a without any explanation and posted after words a couple of formulations for niyyah. In that link they seem to show the acts of prayer from a fiqh perspective which might not be easy to follow if you are not familiar with the typical order of fiqh books.
The correct order of prayer -in practice- however is making the niyyah, saying Allahu Akbar for takbirat al-Ihram (the takbeer to start the prayer) and performing the du'a al-Istiftah (if it is considered as sunnah), then start the recitation of al-Fatihah etc.