Actually the examples are different;

How is this writer's technique called in English? I can answer for the first example but not for the second.

The first example being written in the Second-Person.

The second-person point of view belongs to the person (or people) being addressed. This is the “you” perspective. Once again, the biggest indicator of the second person is the use of second-person pronouns: you, your, yours, yourself, yourselves.

You can wait in here and make yourself at home.

Or in the case of St Paul

Now you, if you call yourself a Jew; if you rely on the law and boast in God; if you know his will and approve of what is superior because you are instructed by the law; if you are convinced that you are a guide for the blind, a light for those who are in the dark, an instructor of the foolish, a teacher of little children, because you have in the law the embodiment of knowledge and truth— you, then, who teach others, do you not teach yourself? You who preach against stealing, do you steal?

Ref Grammarly

The second just being, well what? A piece of writing. It has been described as

Here the speaker is addressing his audience

So I would think it is fair to describe this as a "Speech"

You is used in two question during the speech but it certainly does not do enough to designate this as being written in the second-person

speech noun (FORMAL TALK); a formal talk given usually to a large number of people on a special occasion: Ref C.E.D.

Actually the examples are different;

How is this writer's technique called in English? I can answer for the first example but not for the second.

The first example being written in the Second-Person.

Also let us define that there is a difference in "Style/technique" and "use".

How the speech or letter is intended to be used, or is used, does not define the style or technique. Either could be used in an "open letter" but that is a use not a "style"

The Second-Person.

The second-person point of view belongs to the person (or people) being addressed. This is the “you” perspective. Once again, the biggest indicator of the second person is the use of second-person pronouns: you, your, yours, yourself, yourselves.

You can wait in here and make yourself at home.

Or in the case of St Paul

Now you, if you call yourself a Jew; if you rely on the law and boast in God; if you know his will and approve of what is superior because you are instructed by the law; if you are convinced that you are a guide for the blind, a light for those who are in the dark, an instructor of the foolish, a teacher of little children, because you have in the law the embodiment of knowledge and truth— you, then, who teach others, do you not teach yourself? You who preach against stealing, do you steal?

Ref Grammarly

The second example just being, well what? A piece of writing. It has been described as;

Here the speaker is addressing his audience

So I would think it is fair to describe this as a "Speech"

You is used in two question during the speech but it certainly does not do enough to designate this as being written in the second-person

speech noun (FORMAL TALK); a formal talk given usually to a large number of people on a special occasion: Ref C.E.D.

Actually the examples are different;

How is this writer's technique called in English? I can answer for the first example but not for the second.

The first example being written in the Second-Person.

The second-person point of view belongs to the person (or people) being addressed. This is the “you” perspective. Once again, the biggest indicator of the second person is the use of second-person pronouns: you, your, yours, yourself, yourselves.

You can wait in here and make yourself at home.

Or in the case of St Paul

Now you, if you call yourself a Jew; if you rely on the law and boast in God; if you know his will and approve of what is superior because you are instructed by the law; if you are convinced that you are a guide for the blind, a light for those who are in the dark, an instructor of the foolish, a teacher of little children, because you have in the law the embodiment of knowledge and truth— you, then, who teach others, do you not teach yourself? You who preach against stealing, do you steal?

Ref Grammarly

The second just being, well what? A piece of writing. It has been described as

Here the speaker is addressing his audience

So I would think it is fair to describe this as a "Speech"

speech noun (FORMAL TALK); a formal talk given usually to a large number of people on a special occasion: Ref C.E.D.

Actually the examples are different;

How is this writer's technique called in English? I can answer for the first example but not for the second.

The first example being written in the Second-Person.

The second-person point of view belongs to the person (or people) being addressed. This is the “you” perspective. Once again, the biggest indicator of the second person is the use of second-person pronouns: you, your, yours, yourself, yourselves.

You can wait in here and make yourself at home.

Or in the case of St Paul

Now you, if you call yourself a Jew; if you rely on the law and boast in God; if you know his will and approve of what is superior because you are instructed by the law; if you are convinced that you are a guide for the blind, a light for those who are in the dark, an instructor of the foolish, a teacher of little children, because you have in the law the embodiment of knowledge and truth— you, then, who teach others, do you not teach yourself? You who preach against stealing, do you steal?

Ref Grammarly

The second just being, well what? A piece of writing. It has been described as

Here the speaker is addressing his audience

So I would think it is fair to describe this as a "Speech"

You is used in two question during the speech but it certainly does not do enough to designate this as being written in the second-person

speech noun (FORMAL TALK); a formal talk given usually to a large number of people on a special occasion: Ref C.E.D.