Is your feature request related to a problem? Please describe.
According to the discussion in #4132 , would be nice to update:

1. Still defining _iteration() as a regular method, but unify all the self.XXX and engine.XXX to engine.XXX. Because (1) as you said users can easily copy-paste our code, (2) maybe someone will override the engine run logic someday and pass other engine as parameter instead of self: https://github.com/pytorch/ignite/blob/master/ignite/engine/engine.py#L859.
2. Check all the engine: Engine functions, if having MONAI specific logic, change the typehint to Workflow.