Hearsay is testimony regarding a statement about a fact, presented to establish that fact. That is, there is some alleged fact, and Person A claims that Person B made a statement about the fact, and the testimony is presented to establish that fact. If Person A testifies about Person B's statement, for the purpose of testifying about the statement itself, rather than the thing that Person B's statement was about, that's not hearsay.

For instance, if I testify that the defendant came into the bank I was working at and said "I have a gun, give me all your money or I'll shoot you", my testimony is not hearsay if the intent of the testimony is to establish that the defendant threatened me. If the intent is to establish that the defendant had a gun, then it would (putting aside the Statement Against Interest exception) be hearsay. I can testify that the defendant threatened me, because I directly witnessed that. I can't testify that the defendant had a gun, if my only basis for believing that was the defendant's statement, because I didn't directly witness that. I can give statements about anything I witnessed, even if those things are themselves statements by other people, it's just that the prosecution can't use those statements by other people as evidence for the things the statements are about, rather than just the statement itself.

So let's look at the examples of "hearsay" that you give:

a number of statements by Trump attorney John Eastman.

Too vague to say whether that's hearsay.

Pence's statements to Trump that he wouldn't try to subvert the election

The only way this would be hearsay is if it was presented to establish the claim that Pence would not try to subvert the election. If it was presented merely to establish that Pence claimed that he wouldn't try to subvert the election, then it is not hearsay. Knowing whether Pence said this is useful both for evaluating Pence's actions, and for evaluating the actions of other people who heard him say this.

As for why this would be preferred to direct testimony, which is more compelling: someone claiming that they said they wouldn't do crime, or someone else saying that that person said they wouldn't do crime?

Hearsay is testimony regarding a statement about a fact, presented to establish that fact. That is, there is some alleged fact, and Person A claims that Person B made a statement about the fact, and the testimony is presented to establish that fact. If Person A testifies about Person B's statement, for the purpose of testifying about the statement itself, rather than the thing that Person B's statement was about, that's not hearsay.

For instance, if I testify that the defendant came into the bank I was working at and said "I have a gun, give me all your money or I'll shoot you", my testimony is not hearsay if the intent of the testimony is to establish that the defendant threatened me. If the intent is to establish that the defendant had a gun, then it would (putting aside the Statement Against Interest exception) be hearsay. I can testify that the defendant threatened me, because I directly witnessed that. I can't testify that the defendant had a gun, if my only basis for believing that was the defendant's statement, because I didn't directly witness that. I can give statements about anything I witnessed, even if those things are themselves statements by other people, it's just that the prosecution can't use those statements by other people as evidence for the things the statements are about, rather than just the statement itself.

So let's look at the examples of "hearsay" that you give:

a number of statements by Trump attorney John Eastman.

Too vague to say whether that's hearsay.

Pence's statements to Trump that he wouldn't try to subvert the election

The only way this would be hearsay is if it was presented to establish the claim that Pence would not try to subvert the election. If it was presented merely to establish that Pence claimed that he wouldn't try to subvert the election, then it is not hearsay. Knowing whether Pence said this is useful both for evaluating Pence's actions, and for evaluating the actions of other people who heard him say this. Any time you're dealing with a conspiracy, who said what to whom is going to be an important issue; that someone made a statement is an important fact, apart from the claims mad in the statement, and so it will be valid for people to testify to the fact that the statement was made.

As for why this would be preferred to direct testimony, which is more compelling: someone claiming that they said they wouldn't do crime, or someone else saying that that person said they wouldn't do crime?