The googlest thing ever. Typically English words that are borrowed from French and would take “the most” as a modifier because that’s how it’s done in French whereas English or other borrowed words take “est”. It means the same thing. With words like Google, you could do it either way but as a native speaker the most sounds better with this particular word to me.
To say the second meaning it would be phrased more like “this is the most Googlest news week” or “this is the most Google news week”.