Ujm
How it’s supposed to go and how it will go is not necessarily the same way. As you know I am divorced and remarried. So I probably have a little bit more clarification on some of this than others.
First of all a get is usually written by a Rav who is an expert, not necessarily by an official bais din. Said Rav acting responsibly will not immediately write the get but require assurances from rabbanim involved in the case, that the marriage is beyond salvage, prior to writing the get.
Now this is a case involving both parties wanting out. Your specific case I can only guess at. But logically Rabbanim will get involved. They can’t force either party to stay married and at some point in time will pronounce the marriage unsalvageable and push for a get.
It makes sense to do it get. Bc a couple that is married but not living together is a couple in danger of committing other averos.
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