Do you agree with "to clarify" ?

"Just to clarify" sounds good to me. "Just to confirm" would also work. I'm guessing you are talking about something like the context of a work meeting?

Your original statement is fine it's just verbose. You could just say "Just to confirm" on its own, and the "my understanding is correct" part is assumed. However, in my opinion "(Just) to clarify" is slightly different: "Just to confirm" implies you have an understanding that you think is correct and you just need them to say, "Yes that's right," or else correct you. "Just to clarify" implies you have a confusion about what you have been told and you need someone to confirm what they mean. You might have an assumption of the right way to interpret them but you're not sure enough.

If you don't fully understand something you were told, you could say: I need some clarification on this. Do you mean........? To clarify, do you mean.......? Sorry, I'm unclear on your instructions. Did you mean......? Can you clarify a little? I'm not sure what you meant by...... Edited to add: Either person in the exchange could "clarify" the information given. If I were the one receiving the message, I would rephrase what I was told slightly to make sure I have the correct information. The person sending the message could do the same thing if you just ask for more information.

I tend to use, “So, to summarize…” The ones you listed are fine, though.

yes, ‘to clarify’ is fine. more importantly, please don’t use grok to learn english.

"To confirm" means the person is fairly certain they understand. "To clarify" means they want to ensure they both understand, clear up any subtleties, that's there is no ambiguity.  "To ensure I've got it right" is not concise.

I also like using "as a coherency check, ..." at my job. "As a coherency check, I'm supposed to bring these papers to legal?"

Yes

right? is the most concise way

> From my knowledge, to clarify means you’re the one providing information that’s potentially unclear, and you want to make it clear This is not wrong, you can use "clarify" in that way. You can also use it if someone else is providing information and you're asking them to clear it up. Both uses are correct

I've only used "to clarify" when I think the instruction I gave earlier wasn't as simple or straightforward as it could have been. If I'm asking, I would say "to verify", or just restate what they said in my own words as a question: "Just to verify, you want me to paint this wall Rambling Rose?" Or, even, just prompt for them to tell me what they want: "what would you like me to do with this wall again?"

Depends on if you follow it with a statement or a question.

You could say 'may I check' or 'may I double-check' and then repeat your understanding of what was said before the other person confirms. 'Did I get this right?' could also be used. Less formally 'ok, so (repeating what you think was said)'. There are many ways of doing this, but perhaps not enough people DO check!

To clarify does mean make what’s unclear clear, but in this situation it also is fine most of the time. In use, as the responding person I would probably have some confusion or uncertainty on some specifics, so clarifying them might mean simplifying or redacting to necessary information to avoid any confusion. “To ensure I’ve got it right” is more accurate wording to that, but both can be used and will be understood. The latter isn’t something I personally would say, but I don’t find myself in formal settings often. “Just making sure,” “you meant (x) right?” Could be some informal options. There are a lot of ways to say this.