The first string is consistent with Steam on other OSes and is not a linux-specific issue. Checking for video driver updates has been removed from the linux client.
If you want to pursue this further, please contact steam support.
Nothing extracted yet.
Please post in comments all strings that doesn't make sense anymore
my batch:
settings → interface | Run Steam when my computer starts # This should be more like "... when I log in" or "... when my desktop environment starts"
Steam → Check for Video Driver Updates... # This shouldn't appear on unsupported distributions