Command teleport using relative coords changing dimension applies coordinate_scale only to the relative.

Stand in the over world at 800 64 800 use this command:
execute in minecraft:the_nether run tp @s ~ ~ ~
...and you will NOT be at the exact same coordinates, but at 1/8th the coordinates -> 100 64 100.

Stand in the over world at 800 64 800 use this command:
execute in minecraft:the_nether run tp @s ~800 ~ ~800
...and you will NOT be at the added coordinates, nor will you be at the 1/8th of the added coordinates, but instead you will be at 1/8th the relative plus the full additional 800 -> 900 64 900.