I am not from US or western, and I never see this kind of style in my place. My country more or less retain the traditional format.
But I have seen the similar elements
In presentations or teachings of Dharma there is a structure where someone in the audience requests the teaching.
In Theravada tradition, this is done through chanting a paritta called aradhana dhammadesana (requesting dhamma sermon). Before that, usually there is requesting refuge and sila.
In Tibetan tradition, this is done through the ritual of offering mandala. Followed by offering symbols of the Buddha mind, speech, and body (small stupa, a scripture, small Buddha statue).
If you want to see the example, search for Dalai Lama 14 public Dharma talk.
I have not seen Eastern Mahayana tradition doing this. Usually they just directly give the teacher the time to talk.
The presentation proceeds, typically prefaced with an articulation of the lineage, establishing the authority and reliability of the teachings
I have never seen this.
The most similar thing I know is the Lamrim four outline. Lamrim is Gelugpa sect curriculum, stages of the path to enlightenment. This structure is said to be copied from ancient India university Vikramasila
- Establishing the purity of the source (biography of Buddha and the subsequent teachers that passing down the teaching. Usually only cover the most important one)
- Establishing the purity of the teaching itself
- Correct method to teach and listen to Dharma
- The actual instruction.
Because teacher usually repeat the structure (mentioning 1 2 3) before going into detail of the teaching which is contained in point 4, this could be mistaken as above.
The tradition that emphasize lineage usually came from Tibet or Zen tradition.
There is usually an invitation by the teacher, to the audience, to establish one’s intentions, what one wants to get out of hearing the teachings and how one intends to implement the teachings.
I have only seen this in Mahayana sutra.
In my experience, the topic is either set beforehand, or left undetermined - up to the teacher to choose.
There is the teaching, some time for questions, some time for reflection, and some form of benediction to end the teachings.
This one is very general and happen in all tradition.