Based on Example 4 on page 18 of IRS Publication 970, it appears that you can include the spring semester tuition in the expenses used to calculate the American Opportunity Credit. However, you didn't say when you paid the tuition for the spring semester courses. On your 2024 tax return you can only include expenses that you paid in 2024. If you paid the tuition for the 2024 spring semester in 2023, you cannot use those expenses on your 2024 tax return.
All of this might not matter, though. If the fall tuition was $4,000 or more you will get the maximum credit just based on that. Additional expenses above $4,000 would not give you any additional credit.