Where does Egg Heist take place?

The location matters because of what the mode does with it. Egg Heist, also called Diamond Egg Theft, is an extraction mode. You are dropped in, you fight, and then you have to leave with what you took. The islands are the arena for that, and your exit is an escape boat.

It is a multiplayer mode mixing PvP and PvE, so the opposition is both other players and the game's own creatures. The eggs are the prize, and getting out with one is the whole point rather than a side objective.

Getting off the islands

Extraction is the vulnerable part. You make the trip back to an escape boat, and a Pathfinder can extract safely once one personal objective is complete. That objective is either personally submitting one Aniimo Egg or personally collecting a set number of Eggshell Coins.

The coin number is not published. It was significantly reduced in the February 4 update, so the coin route is less work than it was earlier in the beta. Note the word personally in both conditions. A teammate doing the work does not clear your objective for you.

Carrying the giant egg

The central giant egg changes how you cross the islands. Whoever collects it transforms into the egg itself in order to extract it, and in that form you have no combat abilities at all.

That makes the carrier entirely dependent on the rest of the team. Your teammates have to escort you all the way to evacuation, because you cannot fight back on the way. Deciding who takes the central egg is a team decision about who you can afford to have out of the fight.

Not settled: The region's name appears in two forms, Lost Islands and Lost Isles. Nothing beyond the region name is published yet: no map layout, no number of islands, and no word on whether other modes use the same ground.