I took the trouble to read such 2007 travel deal and I was surprised to read that tourist visas are never mentioned. From my (academic) point of view, the deal mainly involves scientific and student exchanges.
The above news piece (and many others) mentions the growing outrage at Russians citizens entering the EU for "holidays and shopping" and that the message should be that "it's not business as usual" in the relations with Russia. But the suspended deal has nothing to do with holidays and shopping.
Admittedly, the accepted answer here mentions studying abroad as a luxury good worth being cut off to Russian elites, but the visa deal refers to short-term stays. I imagine that the socioeconomic demographics of "elites studying abroad" and "normal students doing short exchanges" are different.
So what is the real (intended) effect of the ban? One could identify with some punishment to (typically nationalist) Russian billionaires, but I think that students and scientists willing to do exchanges abroad are within the most progressive citizens that would benefit from a global view and could convey how the war is seen in the rest of Europe when going back home. Maybe this is too naïve a view?