Maybe I am crazy but to understand something that does not exist we all must be a bit crazy so here it goes.
I think eldritch beings are not entities above us but bellow us. Think of the human mind as a house, the floor is the logic of our world being the base of everything we are, the walls our reason being able to ignore everything that we believe that is not true. the door is our way accepting new knowledge that does not conflict with our reason (walls).
Now when we think of an eldritch being, we think of a being so much greater than us that we cannot comprehend, but I don’t think that’s it because us humans have had things that we weren’t able to comprehend before and even beings that we didn’t truly understand of control (if we assume gods and spirits were real), I believe that eldritch beings are beyond the logic of our world but not because they live in a higher dimension but because they live below the base of all dimensions way past the floor of our house that is the logic of our world. If we view an interaction of an eldritch being as a natural phenomenon I think we should compare it to a earthquake or a rift, making our whole house tremble making the furniture that is our memories and thought shift and break, making the walls of our reason crack and let in knowledge that our brain cannot simply accept and even make the floor of our house crumble and making us fall outside our own mind in a place completely indescribable not because we haven’t been there before but because it’s simply outside of the understanding of our mind.
As for the people that sometimes survives this rare hypothetical encounters but they change irredeemably I believe this can be explained by this analogy too: a house can be repaired, if the walls break it can be patched, if the furniture shifts, breaks or disappears it can be moved back, repaired or even substituted and a floor that has crumbled down to something deeper it can be rebuilder and make the walls taller to reach the place of the previous house. But even if you do that it levees scars, the floor has scratches of the furniture being moved of the floor, the repaired objects have cracks, the now objects are not exactly the same (not as old or not with the same wear and tear), the walls show were they cracked with newer paint or weaker/stronger parts and if the floor came down the hose dimensions will be completely new