Is a woman considered sinful if she requests a divorce from her husband whose manners and actions she dislikes, who mistreats her, and who threatens suicide when she asks for separation, despite her having performed Istikhara and expressed her desire to him?

A woman is permitted to seek divorce from her husband if he wrongs her or commits فسق (transgression/immorality). As long as your husband threatens suicide and claims to worship you, this is evidence of the weakness of his faith. We advise you to try to reform him by encouraging him to attend religious gatherings and associate with righteous people, cooperating with him in acts of obedience, being a good wife to him, and making abundant supplications. If these attempts are not fruitful, then there is no blame upon you in seeking a divorce.