When wyatts kidnapped, all his friends are murdered. He’s the only one that ‘survives’
He can’t be sensed or found because the town he’s in is surrounded by the bones/bodies of thousands of witches killed by demons. It’s an act of evil so powerful it causes a blind spot in the world. No one knows the town exists and it, and those in it, can’t be sensed or found by magic.
Wyatt’s mannerisms are similar to the comic version of The Winter Soldier/Bucky Barnes. He’s working simply for the bad guy, living for them. He’s Lucifers’ weapon, nothing else. But that IS his life, he’s very loyal to them, he knows nothing else. It’s not something as simple as being controlled or brainwashed (though he has slightly been through the trauma and torture he faced). It’s just who he is now. Take this video for inspiration and how he acts when he’s not ‘ working ’. Demons, weirdly enough, are his family. His friends. He’s loyal to them and Lucifer alone.
Eventually his family do find him and remind him of who he is. But being, virtually, raised by Lucifer from the cage (the only person he had to talk to) Wyatt can’t destroy the connection he’s formed with him. He doesn’t like it, but he’s always seen him as his father as Lucifer, tauntingly, has always treated him like his ‘son’. (interactions where he’s ‘good’ again and trying to redeem himself will only take place through plotting or request. The default will be ‘weapon’ Wyatt).
When Wyatt does come back to his senses he loathes Lucifer. He destroyed his life, everything good about him. It’s just a big old complicated mess. And while he wants him dead, deep down, he doesn’t know if he can do it himself.
Eventually, he doesn’t feel comfortable being with his family anymore. The connection there is broken and he’s done so much that he feels undeserving of them, but also, totally wrong acting as this ‘warrior for good’ when he’d done so many horrible things. Vanishing one day with nothing but a note telling them not to look for him. Wyatt starts up his own bar/semi-roadhouse in the middle of outback america that acts as a respite for all magical and supernatural creatures. Hunters are welcome so long as they mind their own business and don’t hurt any of his customers. He changes his name, especially his last name, and doesn’t hunt or fight evil anymore. He’s just impartial to it all and totally neutral only providing information if its needed. All he wants is to finally live as his own person without any side pressuring him to be theirs. (this is after either, Lucifer being sent to the cage or after he’s killed in s14).
In this specific verse, Wyatt IS half angel half witch. THIS HC explains it further but essentially Leo was one of heavens angels that was thought to be killed by Lucifer in the uprising. However, he just used that opportunity to live amongst humans ─ changing his name to Leonardo Wyatt and becoming a guardian angel for witches. Eventually, he falls for Piper and Wyatt is born ( along with Chris and Mel ) but he gives up his grace for his family just like in the show, becoming human.