It depends. If your spouse is non-resident of DE and had no DE source income then they do not need to file a DE tax return. Here is an extract from the DE PIT-NON Instructions.
"Non-Residents – File a tax return if you have any gross income during the tax year from sources in Delaware. If your spouse files a married filing separate return and you had no Delaware source income, you do NOT need to file a Delaware return."
However, if there is either DE source income or your spouse is a DE resident and their income exceeds $9400 for 2023, then they would have a filing requirement. DE residents have options to file completely separate returns (filing status 3) or file separate returns on a combined form (filing status 4) or of course a joint return (filing status 2).
Here are the instructions for DE PIT-RES forms for more information.
"Generally, separate returns (filing status 3 or 4) will be advantageous if both spouses have Delaware adjusted gross income in excess of $9,400." - DE PIT-RES instructions.