Whenever I google for "bass fretboard notes" or similar, though, I get images with all notes in capitals (E,A,D,G) as if they were the same.
I assume you mean a diagram like this one:
Generally, people who use these diagrams already understand what the intervals between the strings are, and that each fret is a semitone higher. Which note position is in which octave - at least relative to the others - will more-or-less already be clear to them; they just want to put note names to the 'patterns' they already know.
It's true that you could perfectly sensibly add an octave designation to such diagrams, but this extra information just wouldn't add much value for most people who would consult this kind of diagram.
Let's contrast this with the first diagram that I get when I google "isomorphic keyboard":
Most people seeing that for the first time won't understand the interval patterns; the octave numbers in that case are much more useful to more people.
how do you distinguish e.g. the "E" of the plain E-string from the "e'"(?) on the 9th fret on the g-string?
When people are notating how to play a piece, they may use tablature, or standard notation with positions indicated with Roman numerals. When they're talking casually, they may just say 'E on the 9th fret on the g-string'.
The thing is - neither Helmholtz notation nor scientific pitch notation provide a complete solution to this problem, because 'E on the 9th fret on the g-string' is the same actual pitch as 'E on the 14th fret on the d-string'.
In situations where we do want to specify pitch, I'm much more used to seeing Scientific pitch notation than Helmholtz notation. In our brief exchange in the comments, we already highlighted two ways that Helmholtz notation can be confusing; https://en.wikipedia.org/wiki/Scientific_pitch_notation#Use mentions some other problems with Helmholtz notation too.