You had to file for the extension, plus pay enough to cover your whole 2023 tax liability, by the April deadline. Once you file for an extension, then you have to actually submit your return by October 15.
If you didn't file for a federal extension in time, then there's a good chance your state taxes are also late. Definitely go ahead and file ASAP, because the longer you wait the more you will accrue late penalties and possibly interest.
If you don't owe any money (meaning you expect a refund), you might owe a late filing penalty, but you shouldn't owe interest.