Is it permissible to seek forgiveness (istighfar) with the intention for Muslims, and is the formula "O Allah, You are my Lord..." permissible with the intention for Muslims?

The encouragement to seek forgiveness for believing men and women is mentioned in His (Allah's) saying: {And ask forgiveness for your sin and for the believing men and believing women} [Muhammad: 19]. And in the saying of the Prophet, peace and blessings be upon him: "Whoever seeks forgiveness for believing men and women, Allah will write for him a good deed for every believing man and woman."

A servant can seek forgiveness for himself and for the believers. The wording of Sayyid al-Istighfar (the master supplication for forgiveness) has a special virtue. As for the phrase "Astaghfirullah (I seek forgiveness from Allah)," if a person says it intending it for himself and all other believers, what he intended may occur, but mentioning the believers verbally is more preferable.