I'm so glad this manga is trying to show proper pet care, but as your resident fish nerd I must add some of my own comments to Tadano's advice:
Goldfish actually get huge and live for decades with proper care, so they aren't easy pets. So many people get bad advice when sold fish as pets so it's sadly a common misconception that they just live in bowls... To really thrive goldfish should have at least 10 gallons(38L) of water per inch of body length, so a bowl is never an appropriate home for one.
He is right about the dechlorinator and the water needing to be oxygenated though. Some toxins in water don't just evaporate from letting it sit out, so using water conditioner drops every time you change the water is necessary to remove chlorine and other bad things. And goldfish need a lot of oxygen so a bubbler/pump will help, but what's really important is having enough surface area at the top of the tank for proper gas exchange, which is almost impossible in a drum bowl like Manbagi's. Another reason the bigger the tank the better!
And finally, the most important thing that ALL pet fish need is a filter! Just bubblers and changing the water aren't enough because when fish poop in the water or when leftover food breaks down it creates ammonia, which is toxic even in small amounts and can greatly harm the health of the fish if they have to swim in it (aka breathe in it) for any prolonged period... This is why so many fish in bowls die so early instead of living out their full lifespan being healthy & happy. Having a biological filter establishes a bacteria colony that breaks down the ammonia into nitrates (the nitrogen cycle). What Tadano put in her tank looked like a filter though so that's good.
Even in a properly filtered tank, I still recommend changing the water 25-50% each week.
Sorry for the wall of text lol I just wanted to make sure that if anyone gets a cute goldfish like People-kun they remember to do research on the care needs and don't just keep em in a bowl :')