1098-T the scholarship amount is $22,000. Do I split this in half (11,000) to reflect that half was for the fall 2021 semester and half was for the spring 2022 semester?

You should enter the 1098-T in TurboTax the way it is listed on the form. Then, if there is scholarship income reported in box 5 that was used to pay for tuition that is paid in 2022 and therefore not listed on 2021's 1098-T, reduce the scholarship income reported in 2021. You do this by editing the scholarship entry on the screen that says Here's Your Education Summary. Click the Edit option next to Scholarships and enter a negative figure equal the scholarship money used to pay the 2022 tuition on the row that says Other Scholarship/Grants/Fellowships. 

When you get next year's 1098-T form, you need to make sure you account for the scholarship income you applied to 2022 since otherwise you may overstate your education expenses.