I lived in Delaware in 2023 for 6 months, & then moved to Georgia the last 6 months of 2023. Delaware has no state taxes, how is it I owe Delaware $1000? GA refund is $72

Where are you getting the idea that DE has no state income tax?   Delaware does have a state income tax.

The states without a state income tax are:

Alaska, Florida, Nevada, South Dakota, Tennessee, Texas, Washington and Wyoming

You need to file part-year returns for DE and for GA.

https://ttlc.intuit.com/questions/1901227-how-do-i-file-a-part-year-state-return

https://ttlc.intuit.com/questions/1901560-how-do-i-file-if-i-moved-to-a-different-state-last-year

https://ttlc.intuit.com/questions/2895983-how-do-i-allocate-split-income-for-a-part-year-state-return

https://ttlc.intuit.com/questions/1901267-which-states-don-t-have-income-tax

Nine states — AK, FL, NV, SD, TN, TX, and WY — levy no state income tax. NH has a tax on dividends and interest . WA started taxing Capital Gains in 2023. Leave boxes 15 thru 20 blank (empty) on the TurboTax W-2.

DE has no sales tax.

Delaware does not have sales tax, but it does have income tax.  

For more information, please see this TurboTax Help Article: How do I file a Part-Year State Return