Turkeys are not as fussy about their home as chickens.
I build a "turkey house" for mine. Very few use it, Some refuse to go in it. I have never lost an adult bird to a predator, even when they sleep outside. Left to themselves they will find a tree or fence they like to sit on.
Ethel if left to her own would roost with the chickens. She has a couple smaller turkey hens that follow her. Last winter I had 5 birds that never went into a coop or pen. They sat out on the fences, trees or rooftops. I live in a very rural area surrounded by "holy land" ( Federal government wildlife refuge that is illegal to even step in let alone kill a predator in). I have terrible predators, I lost 20 chickens or more last summer to predators. I lost some baby turkeys no adults.
I guess I am trying to say, do not over think what it needs for housing. Locking her up is harder on her than running free is. Turkeys really are social and want to be with people.
I force my turkeys into a covered run now, but that is more to get them use to it for when I have poults. Poults need to be protected until they are nearly fully grown. Things like to eat poults.
Your turkey will follow you like a dog. I let my turkeys out of the pen when it gets light. They explore and do their thing all day. When I step out my door, they come running. It is like 20 little raptor (dinosaurs) running to greet me. If I do not spend enough time outside, they sit on the deck rails and look in the windows to see what I am doing.
Once she learns where home is and who her people are she should stay there. Makes me wonder where she came from and why? How far are your neighbors? Do any of them have turkeys? Are there wild turkeys in the area she could have followed and got lost?
Most of us with turkeys if forced to make a choice between turkeys and chickens would give up chickens.