I have about $750 of freelance income reported on 1099-NEC, remote working from AZ and the PAYER is in DE. Do I file state taxes to DE in addition to AZ?

If you never worked or lived in Delaware then you only report the income on your Arizona resident state tax return.

And this is the case even though DE goes by the "convenience of the employer" rule?

Only if you went to DE to do work.   The income is sourced in the state you performed the work in.   The payer's location doesn't matter.  

The convenience of the employer rule doesn't apply to you as an independent contractor; the payer is not your employer.