Housing market affordability is so bad that Zillow says it will take you 13.5 years to break even on a purchase from July onward

Zillow over payed for houses, then couldn't sell them as quickly as expected because the COVID housing market took a down turn, and so they sold them at a loss, lost millions of dollars, and closed the house buying business. They also made plenty of low offers or under-payed for houses at times. They were trying to break even on home value on the hole, but couldn't reign in the wild swings of gains and losses. Their entire business model was based on the seller fees, not on the house value.

In any case, they closed that business in 2021, and has since sold the rest of their inventory.

I don't see how that would have a lasting effect on housing prices though. I'd attribute it more to a housing shortage due to people buying up real estate, and keeping it as rentals. Even when operating, Zillow aimed to resell houses within 3 months, not hold on to them as investments.

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"That’s what one real-estate agent claims in a video that went viral on the social-media platform TikTok"

Hardly a compelling source.

" he’s suggesting that companies such as Zillow are using the data they glean from people’s perusal of home listings on their sites to make decisions about which houses to buy as iBuyers."

Based on what exactly? Zillow used publicly available information about houses, just like everyone else does. Zillow traffic patterns had nothing to do with it and really wouldn't even be useful for that. Buying decisions were based on home value and forecasted ability to resell, not derived interest based on page views.

"Gotcher later argues that the company will buy 30 homes at one price, and then purchase a 31st home at a higher price. “What that just did is create a new comp,”"

False. Zillow literally excluded houses that it bought from its comps to avoid that bias. I know because I wrote that code.