There are two reasons in my mind why buybacks are different. The first is that buybacks are reported after the fact and do not directly alter the share price, rather they increase competition for the available shares and reduce dilution. Dividends immediately reduce the share price by the dividend although the price often moves up a little before the ex-dividend rate.
The other reason is that there are very few stocks that are being valued by the market on any sort of model. That goes for cash flow models as well as other things like PE ratios, etc. We are in the tinkerbell regime, prices went up over the last 10 years because people are clapping louder. Obviously that is a controversial take but I am not predicting a reversal, just saying that the market overall is in a weird place.
There's also an open market buyback. And multiple ways of doing it off the open market, often known as a tender offer for a popular method where you get shareholders to bid on the lowest price they would accept within a range of premium buyback prices.
Off the market, an offer does become public immediately, that is a necessary component of doing it at all. The sales do not. Directly is the wrong word, there's no more direct way to affect price than a bid/ask/sale of a share. The key is that the information about how much of the stock will actually get bought at what price is delayed on its way to becoming a price signal in the market.
The other reason is that there are very few stocks that are being valued by the market on any sort of model. That goes for cash flow models as well as other things like PE ratios, etc. We are in the tinkerbell regime, prices went up over the last 10 years because people are clapping louder. Obviously that is a controversial take but I am not predicting a reversal, just saying that the market overall is in a weird place.