I don't consider myself very well informed on this, but checking your links
The purpose of this Agreement is to facilitate, on the basis of reciprocity, the issuance of visas for an intended stay of no more than 90 days per period of 180 days to the citizens of the European Union and the Russian Federation.
So at least it involves short-term visas. True, the agreement doesn't say anything about tourists. While students are mentioned, given the duration, these don't seem to be the kind of visas you'd give to students except for a summer school and the like.
Another bit of the puzzle seems to be that Finland was among the countries that asked for this, seemingly because that would allow them to increase the visa fee, according to Le Monde
Finland, which shares a 1,340-kilometer border with Russia, wants to suspend the short-stay visa facilitation agreement signed between the EU and Moscow in 2007. Some of its provisions had already been annulled after the start of the war in Ukraine on February 24, including the visa exemption for Russian diplomats. Finland wants to go one step further and revoke the agreement, which allowed for a fast-track procedure for processing applications and reduced the cost involved (35 euros as opposed to 80 euros).
Also, they plan to restrict tourist visas (at least those given by Finland itself) by other means:
A quota system will also be introduced – tourist visa applications will only be accepted on Mondays; all other days will be reserved for Russians who have family and friends in Finland, or who work or study there.
Borrell mentioned somewhat obliquely
"It’s going to be more difficult and longer, and consequently the number of new visas will be substantially reduced," said Josep Borrell, the EU's foreign policy chief, at the end of an informal meeting of foreign affairs ministers in Prague.
"This is a common approach and a common approach will prevent potential visa-shopping by Russians, going here and there, trying to [find] the best conditions."
So, I'm guessing they envisage that if tourist visas are reduced by other means, there could be "visa-shopping" by getting other kinds of visas, although TBH given the apparent lack of EU-level agreement on tourist visas proper, I'm not really seeing how "visa-shopping" would be prevented by switching from one country to another (instead of one visa type to another.)
I could not quite an official statement from Finland on the exact reasons they wanted the agreement's suspension, but that they asked for the agreement to be suspended is confirmed from another source citing their MFA Haavisto, but without a quote or details.
Besides the suspension of the agreement, there was a more subtle nod in the EU decision
As a concession to those countries [bordering Russia], ministers in Prague also signed off on a sentence in the agreement that looks rather innocuous at first but actually could end up carrying significant weight: "Given the challenging implications for the bordering countries, we acknowledge that measures can be taken at [a] national level to restrict entry into the EU in conformity with the EU Schengen border code."
This doesn't automatically stop Russians entering at the borders of these five countries, but it does offer the affected countries a chance to cook up a regional solution with the EU's blessing.
A regional solution could come sooner rather than later. On September 2, relevant officials from the quintet of countries directly bordering Russia are set to meet with the aim of coming up with a common approach by next week. An EU source with knowledge of the debate but who wasn't authorized to speak on the matter said that a potential solution could include case-by-case scrutiny of every single Russian attempting to cross their borders. In practice, this means that what once might have taken a few minutes to cross the border from Russia will now take much longer and will, perhaps intentionally, create bigger bottlenecks.
"No tunnels, no corridors" was the mantra repeated by officials over the last few days of negotiations, emphasizing that no exemptions on Russia's borders will be made for visas issued from other western EU countries. Crucially, the visa issue will now be treated like a regional problem, with the Baltic states, Finland, and Poland still having the power to outright deny entry to any individual, even one holding a valid visa.
"National security concerns" will be the official justification, although in truth the reasons are much more political. [...] Latvians will hold parliamentary elections in October, and the Finns and Estonians will go to the polls in spring 2023, and their respective governments are keen not to let visas for Russians become a defining electoral issue.
So it does look they might have a way to interfere with "visa shopping" via different countries as well, at least at the point of admission, although the details haven't been ironed out just yet. Interestingly, RFERL claims there are no "tourist visas" as such for the Schengen zone
Focusing on tourists was always something of a misnomer, as there is no such thing in the EU as a "tourist visa." EU member states can issue Schengen visas for up to 90 days in any 180-day period, a so-called category C visa. These can of course be used by tourists but also by businessmen or Russian truck drivers working for EU companies, transport links that the Baltic states are keen to keep open.
On a quick check with a diff source, the claim does seem to pan out...
The short-stay Schengen visa – type C
Another type of Schengen visa is the short-stay visa (type C). Particularly useful for tourists visiting Europe, it allows the traveller to stay in one or several countries within the Schengen Area for a maximum of 90 days.
Depending on the reason why you are travelling to the Schengen Area, your situation and the visas you have already obtained, these type C visas may include different authorisations and restrictions, which are all indicated on the sticker placed in your passport by the government. These may include: countries, number of entries, length of stay.
It doesn't seem to list the purpose of visit (like tourism) as a restriction, although it's possible the source is not exhaustive on the type of restrictions that may be stamped/applied.