When I entered Russia, my visa was stamped with a blue stamp, and the school sent a new invitation. Will there be any problems in applying for a new visa? Will my visa be refused?

Please ask the school to contact the Immigration Bureau and ask them to issue a Свидетельство to prove that your matter is made up of nothing. Submit it to the embassy together. As long as the visa materials are convincing, the visa officer will let you pass. Or come to the embassy with relevant supporting documents and explain the situation to the visa officer.