is it grammatically correct?
it's been a week already since we were working together.
is it okay to build a sentence like this?

Question

Answer

Yes.  This sentence implies that  you only worked with the other person once, and you don't have plans to work with them again.  If you work with the other person often, and you plan to work with them again in the future, say:
"It's been a week since we've worked together."

Answer

Yes

Answer

It’s very unnatural.
It’s been a week already since we started working together.
We started working together a week ago.
We’ve already been working together a week.

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