The treatment seems to consist of settlement, filtering, aeration, and some absorption. But there doesn’t seem to be heating or bleaching or UV light or whatever that would kill most pathogens.
You’ve come to the right place to ask this question. 
I’m an engineer who works for a water and sewer utility. Our main wastewater treatment plant is across the street from where I am sitting right now.
Anyway, what you are describing is referred to as primary treatment, This was the only treatment there was when wastewater treatment plants were first built in the early 1900s. However, virtually all wastewater treatment plants now include secondary treatment, which utilizes so-called “activated sludge” consisting of microorganisms to consume the waste matter. We recycle the sludge back into the secondary reactors to keep the process going continuously. Some of the microorganisms are aerobic and require oxygen, so we aerate and mix the tanks; others are anaerobic.
There is also tertiary treatment which is designed to reduce nitrogen and phosphorus loading into the receiving water body, but not all wastewater treatment plants have this.
The overall process does reduce much but not all of the pathogens in the wastewater. For much of the year this is good enough. In warmer months when one could expect people to be boating or swimming in the river, we do in fact take the extra step to either chlorinate or disinfect with ozone or UV to kill the remaining pathogens.
Very nice synopsis. When you say “secondary reactors” what are they - ponds or big tanks, or…? And I will totally refrain from any jokes as you have probably heard them all by now.
Secondary treatment tanks are typically large rectangular above-grade tanks constructed of concrete. The flow is directed through the tanks by various baffles and weirs. There are large air injectors and/or mixers in the aerobic areas.
Primary treatment tanks are also typically made of concrete but are usually circular because they have rotating skimmer arm(s) on the water surface and scrapers at the bottom.
The reason that the tanks are usually above grade is because the treatment plant is often in a low-lying flood-prone area that is generally near the receiving water body (because you want the sanitary flow to get there by gravity), and if the area does flood out in a storm event, you don’t want to contaminate the receiving water body with untreated wastewater.
Thanks. Years ago near the beginning of my career I remember making a comment about some bad odors (i.e. like shit) when inspecting a sewage pump station with a contractor, and his response to me was, “You know, I really don’t even notice the smell anymore, and when I do notice it, it smells like money.”
Can I piggyback on this OP (since you are here and all): I read an article about shade balls. Is this covering water that is destined for residential use?
ETA: I ask because it seems like animals and bird poop could contaminate this treated water.
These are used in reservoirs which contain so-called “raw water” that has not yet been treated to make it into potable water. Treated, filtered, and disinfected potable water that is suitable for drinking is never open to the environment for exactly the reasons you state. It is either in a pressurized water main or in a sealed [potable] water storage tank.
In reading the article, it appears they do add some disinfectant to the raw water reservoir, but that is solely to keep down the growth of algae. This bit of disinfectant is insufficient to make it into potable water (plus there are other treatment processes like coagulation and filtration), so this water is still considered to be untreated raw water.
Ideally you don’t have any development around your reservoir, which minimizes any nutrients entering your reservoir (which leads to algae).
is this how San Diego is making waste water “drinkable”?
I know this is, at least partially, blamed on human error, but we had 400,000 people get sick with Cryptosporidium that made it through a treatment plant.
The op was well answered on the first reply so I’ll hop on to mention the receiving streams. Where I work we test the Ohio River for E. Coli throughout the summer (the recreation season). There are a lot of CSO (combined sewer overflow) communities where heavy rains overwhelm the sewer plants capacity so they discharge large volumes of untreated sewage into receiving streams. After a heavy rain it takes about 48 hours for the bacteria concentration to return to safe levels. There is a lot of work ongoing to fix these issues but they are multi-billion dollar efforts that take decades.