What is the ruling regarding a wife's conduct towards her husband if she suspects he practices masturbation, observing his repeated movements of placing his hand on his private parts, and sometimes not performing ghusl afterward, and how can she confront him without embarrassment?

The fundamental principle is to have a good opinion of a Muslim, and it is not permissible to have a bad opinion of him without clear proof, based on the Almighty's saying: "O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin." What your husband is doing does not indicate that he is practicing masturbation, so avoid intrusive thoughts. If you become certain that he is practicing it, then gently alert him to the unseemliness of this act, knowing that masturbation does not necessitate ghusl unless semen is discharged.