Did the Buddha have intention (cetana)?
Arahants don't have karmic intentions and they don't seek any results. They have higher wisdom, higher goodness, higher intelligence that is not possible to measure or described by the ordinary way of thinking. The cause of their actions are not connected to any ordinary human intention, desire or mind state but it happens out of complete purity and wisdom of Nibbana. Even If an Arahant say that "It's my intention" or "It is not my intention" that's only words(which are just tools to communicate with humans) and words have limitations to explain things correctly. So obviously Buddha didn't have intentions but it is not possible to describe the root of an Arahant's actions because they attained Nibbana permanently and Nibbana is the formless state.

A part of this video(5:08-5:35) is about this subject:

https://youtu.be/GRquhvbfVp4?t=308