You want to file for the student as well. The extension for time to file is only for your return. Any money due is still due by the original deadline 4/18/2023. After that penalties and interest will begin to accrue.
You may want to claim the student as a dependent if you qualify for the education credit. A little taxable income to the student vs a big credit for you. You may want to look at another of my answers for help.
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