You are making accurate statements, yes.
The way you are thinking of it is very TAB focused, it seems to me.
To say that the low E of the bass to the Eb/D# above it is the exclusive range of the bass (if both bass and guitar are tuned to standard tuning) is accurate.
You have correctly identified the fret ranges and strings where this occurs.
The cool thing about all this is that the quality of sound still makes the bass sound low. Just the bass tone - what frequencies are pushed.
I’ve often put my P-bass in standard tuning underneath a metal guitar part tuned down to C or Bb (as low as 6th fret E string / 1st fret A string).
When I play the bass at the same octave as these guitar parts, it still adds bass and heft to the line because of the tone and sound and bass-ness.