Does repeating a sin and repenting from it, even after performing 'Umrah for repentance, indicate Allah's wrath? And is there a specific supplication to be said in this situation?

What you mentioned is not proof of Allah's anger towards you. You must continue to repent whenever you sin. If you repent with sincere repentance that fulfills its conditions, Allah will accept your repentance, and it will be as if you never sinned. Allah Almighty said: "And it is He who accepts repentance from His servants and pardons misdeeds." And the Prophet, peace and blessings be upon him, said: "The one who repents from sin is like one who has no sin." So, if you return to sin, the guilt of the sin you repented from will not affect you. And if you return and repent, the effect of the sin will be removed from you. This is the case no matter how many times you commit a sin and repent. You must strive not to return to the sin.