In MN 43, developing any of the samadhi khandha factors (right effort, right mindfulness, right samadhi) is called “samadhi bhavana”.
“doing” samadhi sounds a lot like samadhi bhavana (devleopment) to me. The point is, in the EBT, satipatthana, doing samadhi, doing jhana, they overlap a great deal.
See the suttas on “not neglecting jhana” and “here is a foot of a tree… jhayatha! (meditate)!”. They cover almost all of what you might think of as a satipathana topic or a jhana topic.