Oldenburg suggests that beer gardens, main streets, pubs, cafés, coffeehouses, post offices, and other "third places" are the heart of a community's social vitality and the foundation of a functioning democracy.[6]
The creator of the term himself had pubs and cafes listed as examples of a third place.
He is aware that modern suburbs only offer first and second places with a mandatory car-centric commute between them, and that "public" places have become commercialized to the extent in which one is required to purchase a good or service and is forbidden to "loitering."[8]
Sure the regulation against loitering obviously takes away the convenience nature of third places, but traditionally these places don't enforce the need to spend money to exist in the space. It's also not prohibitively expensive even if you spend money, i.e. its a place where people can conveniently make plans to hang out at.
To your point on capitalism, I've already talked about how capitalism are actively destroying cafes as third places. Starbucks as a notorious example has been promoting drive thru so much, taking away actual indoors space, and destroying the social aspect of cafes. Yes capitalism is bad and malicious in this sense, but a place isn't disqualified as a third place just because you can spend money there.
https://en.m.wikipedia.org/wiki/Ray_Oldenburg
Edit: better formatting
Your original point was that third places require no cost. If you want to change to low cost, then bars and cafes still fit that category.
The average person can afford to order a beer or a coffee during their hangout. I've worked at Starbucks before, in a mall. It's an average of 5 to 6 usd for a drink. The cafe my friend works in is the same. An average place is not serving 12 dollar lattes. The outliers here is some crazy customization, like if you ordered a veinte frappe with cold foam and extra pumps of syrup and subbing whole milk for oat, all that jazz, and the cashier decided to actually ring you up for all of it, or if you decided to go to erewhon.
There is obviously a financial barrier for classifying third places, but that barrier is moreso on the restaurant level in my opinion.
I could talk end to end about how capitalism and world events has led to the slow destruction of the cafe as a third place, but that doesn't mean a traditional cafe and pub is not one. I'm obviously not going to consider erewhon a third place. I'm not going to consider a bar in a penthouse hotel a third place.
Here's an example of UC talking about pubs and cafes being a third place. It even talks about the idea of spending money and free third places.
https://esl.uchicago.edu/2023/11/01/third-places-what-are-they-and-why-are-they-important-to-american-culture/