Is second phrase correct? The main sentence is : No agreement has yet been reached and the negotiations are still ongoing.
"Yet" is an adverb. Adverbs typically precede the words they modify. And yet...
It's not a split infinitive, which is "to [adverb] [verb]"; nothing ever goes between "to" and a verb. But this is similar. Probably a rule, but I don't know what it's called.
You must say "I have not been"; you can't say "I not have been". But you can say "I never have been", "I always have been", etc. But most people say "I have never been", "I have always been", etc. In fact, putting "never" and "always" between "have" and "been" is far more common.
It seems awkward to say "No agreement yet has been reached." But maybe that's just because your alternative, "No agreement has been reached yet" is so common. And I'd say "yet" at the end is far more common than "yet" between "has" and "been".
That's why "always" and "never" (can? should?) go before "has been". But, as I said, that's just not the case (or doesn't seem to be) with "yet."
In many (most?) cases, the position of the adverb affects the meaning.
Only Jim ate the cake. (No one else ate cake.) Jim only ate the cake. (Jim didn't do anything else with the cake.) Jim ate only the cake. (Jim didn't eat anything other than the cake.) Jim ate the cake only. (Nope.)
Always Jim has been a good student. (Nope.) Jim always has been a good student. (Yes.) Jim has always been a good student. (Maybe.) Jim has been always a good student. (Nope.) Jim has been a good student always. (Nope.)
Yet Jim hasn't been a good student. (Nope.) Jim yet hasn't been a good student. (Nope.) Jim hasn't yet been a good student. (Maybe.) Jim hasn't been yet a good student. (Nope.) Jim hasn't been a good student yet. (Yes.)
"Yet" must be one of them irregular adverbs.