I would agree with the grading viewpoints . Not sure there's an easy fix here . That door (as is) may be causing more problems than it's worth . A couple of questions :
1. The BIG question is : Is this the only access to the basement ??? If not , I'd think about eliminating it & restoring the foundation and a proper grade .
2. Is there a pressing need for exterior access to basement , ie: firewood , other ??? If so , maybe an old mode coal/firewood door (w/out stairs , not designed for foot traffic).
Unless you live in a "code-free" zone , I doubt you can put in , say , a 70" (short) door !