The wording of Matthew 5:1-2 is pregnant with meaning :
Seeing the multitudes ...
He went up ... into a mountain ...
and when he was set ...
his disciples came unto him ...
and he opened his mouth ...
and taught them ...
I would say it is quite clear that ascension is in view. 'He went up' and 'when we was set' both lead the mind to contemplate an ascended, seated state, that is to say reminiscent of resurrection and ascension.
And 'he opened his mouth' is unusual. Why say it ?
I would suggest that attention is drawn to the idea of 'mouthpiece'. 'He opened his mouth' emphasises the manner of utterance.
Ascended, he speaks still, by a 'mouthpiece' - his apostles or those who follow the word of his apostles.
'Seeing the multitudes' suggests to me that not just the crowd then present are in view. His eye sees further, into the future. He sees beyond to the whole world.
Risen, ascended, he speaks by the apostolic word and what he says he says to every one that would follow him, as a disciple. Every one who would hear his word and follow him and be obedient to that apostolic word - these are to whom he would speak throughout the church age until the end of time.
The multitude will overhear, true. The whole world will, to some extent or other, overhear what he speaks. But not all will follow in obedience, disciplined to his word.
What Jesus speaks in the chapters called 'The Sermon on the Mount' are famous, worldwide. These words went out to the whole world through the ministry of the apostles.
Yes, I would agree that, initially, the twelve were the recipients. But even at the time, also all the disciples received what he had to say. And even at the time, at least some of the multitude may have heard and passed on to the rest of the multitude what was spoken.
But the words addressed, initially and closely to the twelve (and overheard in the immediate proximity by other disciples) reached even then and reach now, in our own generation, around the planet.
Jesus' last words in Matthew convey the same thoughts :
Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: Matthew 28:19 KJV.
It is the twelve (temporarily eleven) who are to go ... and to teach. They will teach what they had received from him (some of it from the mountain).
Those who receive that word and obey it, they shall baptise. And the baptised shall be taught further ... (v20)
Teaching them to observe all things whatsoever I have commanded you:
So not just the teaching that is sufficient to become a disciple and to be baptised into the body, but all that Jesus gave to the twelve shall be taught to the baptised disciples.
And, lo, I am with you alway, even unto the end of the world. Amen.
It is He who is doing it all.
They (and those who minister their apostolic word) are his mouthpiece on earth as he directs from heaven.