Even with grants and GI bill, you have a financial account at the school (bills. invoices and statements). It's usually online and actual bills are not mailed out. You have to sort it out. You are correct, a large part of your Pell Grant is taxable. Only the portion that pays for "qualified expenses" (tuition, fees, course materials, including a required computer) is tax free. If GI bill is paying for all that, you are safe in declaring all your Pell Grant as income.
page 2 of pub 970:"What's New for 2020 Emergency Financial Aid Grants under the CARES Act. Emergency financial aid grants under the CARES Act for unexpected expenses, unmet financial need, or expenses related to the disruption of campus operations on account of the COVID-19 pandemic, are not includible in your gross income. Because the grant is not includible in your gross income, you cannot claim any deduction or credit for expenses paid with the grant including the tuition and fees deduction, the American opportunity credit, or the lifetime learning credit. See FAQs: Higher Education Emergency Relief Fund and Emergency Financial Aid Grants under the CARES Act."
