Assalamoalikum Warahmatullahi Wabarakatuh
Well, the thing is that there are different opinions that say that the Prophet (PBUH) used to do this and others say that he used to do that. For example, in the Hanafi Fiqh, the rafayadain is not done except one time at the start, If one raises their hands at their ears and says Allahu Akbar while doing so, the prayer breaks. So the Hanafis only touch their hands at their ears at the start of the prayer. While in Sha'fi and Hanbali Fiqh It is necessary to perform the Rafayadain (raise hands above the ears) every time you say, Allahu Akbar. Why? because the Hanafis say that the Prophet (PBUH) did not perform the Rafayadain except for certain prayers while the Malikis and the Hanbalis say that the Prophet (PBUH) always performed the Rafayadain in all his prayers.
What should you, as a layman do?
Choose any Fiqh you find easy to follow because all of them have their own differences.
As for the prayers in Mosques, all 4 Fiqhs have the opinion that despite whatever Fiqh you follow you can pray behind an Imam that follows another Fiqh. For example, If you are Hanafi, you can pray behind a Hanbali Imam and vice versa. That's what happens at Masjid Al Haram because all Imams are Hanbali to the best of my knowledge. The Imam's method of prayer won't affect your prayer. Because at this time and date, It is impossible to determine what was the exact way the Prophet (PBUH) used to pray, etc. thus, you may follow any Fiqh and your prayer will be valid. As whatever the Fiqh you follow is the representation of what the Fiqh's Imam researched and thought the way of Prophet (PBUH) and the Sahaba of doing things was. It may have mistakes, as they were humans but all of them are the best representation of the Prophet (PBUH)'s sunnah, and you don't have to worry about which Fiqh does a certain thing right and which does it wrong, because 1, I or you cannot reach the wisdom of the Fiqh Imams because they were closer to the times of Sahaba and were more knowledgeable than any modern scholar, and 2, what matters is your intention, your way of praying does not matter at this point because whatever Fiqh you follow you will indirectly by following the sunnah of Prophet (PBUH) because none of them is the exactly the same and none of them is completely different from it.
Fiqhas (Sets of Jurisprudence in Islam) are like different rides, you can choose any ride you'd like to go through your journey in the path of Allah (SWT). No ride is the best ride while no ride is the worst, choose the one you please.