This verse begins a section interpolated into the original text around the time of Constantine, created to add the worship and authority of Bishops into the Imperial Cult.
We are on a mountainside because such a high place was considered sacred and a good place to announce great beginnings. Moses went up the mountainside to carve the tablets of Law and place them into the Ark of the Covenant.
“So I made an ark of acacia wood and cut out two tablets of stone like the former ones, and went up on the mountain with the two tablets in my hand.
Deuteronomy 10:3
In this context, Jesus is like Moses – bringing civilization to recalcitrant Hebrews, and those summoned are like his acacia wood and stone tablets, upon whom he will carve the new law.