Praise be to Allah.
The basic principle is that the worshipper intends by saying the taslim at the end of the prayer to exit the prayer, just as he intends to start the prayer when he says the takbir at the beginning.
It was narrated from ‘Ali, from the Prophet (blessings and peace of Allah be upon him), that he said: “The key to prayer is purification, it begins with the takbir and ends with the taslim.” Narrated by Abu Dawud (61) and by at-Tirmidhi (3), who said: This hadith is the soundest and best thing that has been narrated regarding this matter. It was also classed as sahih by al-Albani in Irwa’ al-Ghalil (2/8).
Ibn Rushd (may Allah have mercy on him) said:
The taslim to exit the prayer is like the takbir to start it in all circumstances, because the Prophet (blessings and peace of Allah be upon him) mentioned them together, as he said: “The prayer begins with the takbir and ends with the taslim.”
Just as he cannot begin the prayer except by saying the takbir with the intention of beginning the prayer, similarly he cannot exit the prayer except by saying the taslim with the intention of exiting from the prayer."(Al-Muqaddimat al-Mumahhidat 1/175).
But if the worshipper forgets the intention when saying the taslim, then the most correct view among the views of the jurists is that his prayer is valid, because the intention at the beginning of the prayer includes all of the actions and words thereof.
Please see the answer to question no. 175471 .
Moreover, your bringing to mind the intention to greet the angels with salaam was similar to bringing to mind the intention to finish the prayer and exit from it, because greeting the angels with salaam in the prayer is only done when exiting the prayer. But the worshipper may sometimes focus on one idea more than the other, so it seems to him that he has neglected one of them, but in fact he has brought both ideas to mind.
The basic principle regarding the thoughts that crossed your mind after you said the taslim is that they are mere doubts, and doubts after completing the prayer are to be ignored and do not matter.
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said:
Having doubts after completing an act of worship does not matter, whether you have doubts about the intention (niyyah) or about some parts of the act of worship. That does not matter unless you are certain."(Ash-Sharh al-Mumti‘ 1/206).
To sum up, your prayer is valid, and these thoughts that crossed your mind do not matter. Even if you are certain that you did not form the intention to exit the prayer, your prayer is still valid according to the more correct view of the jurists.
Please see the answer to question #274176.
And Allah knows best.
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