nit: With a buyback, the buyer is the corporation itself, and the cash comes from the corporate treasury. Transitively this is "selling to existing owners", but it's not like their shares are transferred to other shareholders. Rather, the shares cease to exist and the value of all other shares increases to reflect the reduced number of shares outstanding.

Mechanically it's pretty similar to if the company had just paid out cash as salaries (cash leaves the corporate treasury and enters the employee's brokerage account at market values), but the market is the intermediary, and the tax and accounting treatment is pretty different.