Sati parents were killed by The Analyst for her father betrayal. Sati was supposed to be killed too but she was rescued by one of the machines (I forgot name). After that ... she was back in Matrix regularly keeping eyes on Neo in that cafe.
How did The Analyst not notice Sati and kill her?
The Wachowski's style of dropping clues has become very cryptic over the years! but some googling around gave me this on This Is Barry:
The film doesn’t directly answer this, but The Matrix: Revolutions might have a clue. Remember, The Oracle had to find herself another shell and transform herself by losing a part of her code to go into hiding. The Matrix: Revolutions ended with Sati reuniting with The Oracle, and she likely spent many years with her until The Analyst’s new version of the Matrix came into effect. In that time, The Oracle could have taught Sati to find her own new shell. Sati is shown to be able to alter code to create a beautiful sunrise, so it wouldn’t be a far stretch to conclude that with the help of The Oracle, she learned how to alter her own signature and hide in plain sight. The Analyst has no knowledge of Sati’s whereabouts, and considering his overconfident nature, he didn’t think Sati was a threat to him.
Looks like this digital invisibility cloak kept Sati safe from The Analyst. Sati seems to have played a similar trick to conceal herself as The Analyst did to hide Neo.
And exile programs are known to go undetected by Matrix's authority.
As we know from Resurrections that DSI ( Digital Self Image ) could be altered. Sati being an exile and having knowledge of Matrix ( presumably from her Father ) she might have altered her DSI to go undetected from The Analyst.
