I wonder if we should move to an existent jhana thread (e.g. YARVVI Chronicles: V&V, Vitakka = directed-thoughts, Vicāra=Evaluation (of said Vitakka))?
To me the wording of ‘samma-samadhi’ as 8th limb-of-the-path is in a way unfortunate because that group-title appears as an item as well. But okay, a few suttas allow nibbana after the first jhana so technically probably also the first jhana fulfills the purpose to be a last stepping-stone to liberation. Yet, within the four jhana formulas the term ‘samadhi’ appears only in the second jhana.
When I apply this to meditation practice it’s really a game-changer. Investigating dhamma-thoughts or saññās is still something that we kind of know how to do (1st jhana). But to navigate the mind without these tools is mysterious. So to me, this is what your passage refers to @suaimhneas. That “immersion in samadhi” would be equivalent to the second jhana - even though what comes before is not the usually positively described first jhana. It just sounds like an unskillful state of mind.
And why not? Who studies the suttas doesn’t expect total coherence any more. Sometimes the first jhana is described positively, sometimes all jhanas seem to be underemphasized. It always depends on where that particular teacher wanted to push his particular students to.