Along with Russian students, foreign students can apply for a job. However, some issues should be taken into account. In 2020 Russian government has simplified an employment for foreign students. Now to conclude an employment or civil-law contract they need to provide only a certificate from a university (college) confirming that they are studying in Russia.
According to the law, foreigners, who study in Russia, can legally work without a patent or a work permit. And employers, in turn, can hire to work without getting a permit to hire foreign workers. Each foreign student of any university has a right to work.
Nota Bene! You are obliged to terminate an employing contract in case you complete or terminate your education.