No one from school would know that she specifically went to a porn studio. This is the other issue, to be outside that studio to she her go in you have to already be in the Red Light district. Are you really going to gossip about the girls you see while hanging around there?
You are right specifically about the porn studio. A normal unassuming doorway just wouldn't call attention to itself. Unless they had some kind of advertising outside the door saying what was inside it would be walked right by without investigation.
But as for the red light district itself I have three rebuts... basically a big huge essay that can be summarized by saying, "You're wrong. In this game world of Pavlovsk at least they SO would do that especially if it meant a girl was the one gossiped about."
First rebuttal is the easiest. Most gossipers when ashamed to admit their own involvement simply add a degree of separation. "A friend of mine saw", "Someone I know well swears that", "It's true! one of my relatives saw it!", etc.
Second rebuttal is that your point would dismiss most normal (keyword will get into in third rebuttal point) girls from being the origin of the gossip... but the guys? Not every one of them of course, but at least a few would probably brag about visiting a red light district yes. And gossip is not just a girl thing - although admittedly for boys it tends to be more about self bragging and less about cutting down others. IC it would however not be even close to the first piece of gossip that spread from boys to girls - or even vice versa. (See gossip about "someone" - which later becomes a slut shame for Sveta after she actually has sex with those younger boys - watching porn and then having sex with Sveta's brother and his friends as told to the gossiper by her younger brother. See gossip about who various males claimed to have had sex with. Plus countless examples of boys talking about bisexual or lesbian girl encounters.
For that matter, even in a regular school there is almost inevitably going to be at least one person, usually a girl, with a really trashy oversexed rep that the whole school knows about anything she did remotely scandalous. And most boys will probably know about where the strip clubs are at and will brag about going to them despite being under-aged.
I remember when I was in 6th grade one time while changing classrooms I walked by a bunch of boys talking about visiting such a place after school. The reason I bring this up, about half an hour or so after school ended that day I was hanging out where my ride was supposed to pick me up at, but they had called to let me know they were going to be a work for at least another hour. Sitting there bored, I happened to witness a few of those same boys in a group passing by me, and with nothing else better to do with my time I followed them at a distance of a block or two away out of curiosity. Sure enough they eventually led me over to a building that was somewhat hiding on a back alley. It had neon lights saying things like "HOT HOT HOT" "GIRLS GIRLS GIRLS" and pink lips on its blacked out windows which was called if I remember correctly Starlight Emporium Lounge. Or at least it was some fancy name that was way over the top for its location and type of business. I never revisited the place as I had no interest, but apparently those boys and various others in the school did since it was not the last time I overheard someone quietly (or in some cases loudly bragging) talking about the place and rumors of a club nearby the school that featured nudity.
Yes, I never told anyone at school about following them there that day like you suggested about why Sveta wouldn't get told about. But my silence was not because I was afraid of my own rep, but rather because I didn't think anyone would think anything was wrong about those boys doing that, and I felt no need to boost those boys' reps. But if while there that time I had happened to see the school's Miss Popular or some such going in... well, I can almost guarantee you that I'd have told someone. Yes, it is a double standard, But it's one that we all lived with. Or at least in those days we did.
Third rebuttal, what exactly makes you say even the girls are truly not going to admit to it? After all, this is the community of Pavlovsk. A place which even the individual teens living there are well aware is extremely oversexed compared to other regions and even gossips about it. (See gossip pieces about possible Baba Yaga curse, possible demon curse, and a witch who was killed for being too sexual so cursing all nearby to that. See gossip comparing sex rates with Moscow. See gossip about cousins who live outside the region entirely.)
Now, the gossip about this is probably a tongue in cheek way of fourth wall admitting that the usual community is a bit more circumspect than basically a porn game makes them be just to give power to the mighty fap. But taking it as is in an in-character way, the curse itself doesn't even actually need to exist for it to have effected the population. Just by the mere rumor existing it acts as an excuse for behavior. I am going to semi quote a gossiper, "After all if there is a curse then it isn't my fault, right?"
History has abundantly proven that when humans have an excuse for bad behavior, that they then are more likely to become bolder in displaying that behavior. We know for a fact that some girls are uncaring about their reputation when it comes to being sexual beings (see Anushka for example,) and we also know that other girls are very quick to spread gossip (especially Lizaveta) gathered by others.
My points being that even if I tend to agree with your point in a normal school environment, I do not agree with it in this game's school perspective. In a place where people boldly have sex or imitate it in front of everyone, where people actively brag about visiting a brothel (See gossip again.), where girls routinely use their bodies to tease people (boys, other girls, and even adults,) and further wherein the inhabitants are constantly looking for something to say about others (especially if the targets are female,) it all adds up to a summation for me that I personally find too empowered to ignore.
I find it actually bizarre that schoolgirl Sveta could get away with going to the porn studio hundreds of times and risking being seen going into the district twice each time, without
some kind of reputation getting applied. Even adult post-school Sveta I am unsure whether it could entirely be ignored. After all, Bella gets gossiped about merely for being seen going to the city every week. And that's just the city industrial not the red light district, yet even still the gossip claims she's sucking someone off just because it makes the gossip more salacious and with zero proof. (OOC I realize it is a way of warning Sveta's player that singing lessons risks sex acts from the instructor.)
Finally, I honestly feel like you are getting too caught up in the real world rather than remembering that this is an ero world / fap world where different societal rules and behaviors exist. Sveta hasn't a chance to avoid a rep of being a constant weekly visitor to the red light district.