Bring the work, rebuild the settings, and tell your buyers yourself. Nothing transfers on its own, and the parts that cannot transfer are the parts worth redoing anyway.
What to bring
Your photographs, if they are yours and they are good. Up to six per listing.
Your descriptions and measurements, which are the expensive part of a listing and the part most sellers have already written.
Your prices, as a starting point rather than a rule. A different audience prices differently.
What you cannot bring
Your ratings and your review history. They belong to the place that collected them. This is the real cost of moving and there is no way around it: you start as a store with no reviews, and the first few sales are how that changes.
Your follower list. You can tell those people where you went, but you have to tell them.
What to rebuild deliberately
Delivery. Do not copy your old rates across without checking them. Build one profile, set your zones, decide whether you offer collection, and make sure the price covers the parcel.
Your dispatch window. 48 hours unless you set otherwise. Set it to the truth about your week.
Bringing people with you
Announce it where they already are — your group, your stories, the back of your parcels. The thing worth announcing is a specific show at a specific time, not the fact that you have joined somewhere. "I am live on Thursday at 8" gives somebody a reason to arrive.
Do not list everything on day one
A bulk import reads up to 200 rows at a time, so a large catalogue is easy to move. It is still better not to: a new store with five listings and two sales looks alive, and one with four hundred listings and no sales looks abandoned.
Questions people ask
Can I import a spreadsheet?
Yes, 200 rows per import, and a failed row tells you which and why.
Should I keep selling where I am?
Usually yes, at first. Just do not promise the same object in two places.
How long until it feels established?
Until you have reviews. That is a number of sales, not a number of weeks.
More: bulk listing, when an import fails, getting your first followers, selling in more than one place.