Why does this fatwa differ from Sheikh Ibn Uthaymeen’s fatwa regarding the prostration of forgetfulness (sujood al-sahw), where His Eminence holds that one should return to the prayer with the intention of sitting between the two prostrations and then prostrating, while this fatwa mentions starting directly with the tashahhud?

There is no contradiction between the fatwa on the website and the fatwa of Ibn Uthaymeen, may Allah have mercy on him. Both indicate that whoever forgets something in the last rak'ah of their prayer must perform it and what comes after it, and whoever forgets a pillar in a rak'ah other than the last one must perform a complete rak'ah. Doubts after finishing an act of worship have no effect, but whoever is certain of having omitted something must perform it.