Is Dhamma-thinking considered wise attention?

Only Ariya Puggala (Sotapanna and avove) has the Yonisomanasikara.

Is Dhamma-thinking considered yoniso manasikara or wise attention or appropriate attention?

If yes, then why is it not useful, without internal tranquility of awareness (cetosamatham)?

You can be an expert at reciting suttas (or what is known elsewhere as rule-governed behavior), but you also need the direct experience of the theoretical concepts for developing the dhyanas, or pranja. (A healthy morality doesn't hurt either, for that matter.)

For reference, i recently wrote an answer to another question. I hope it applies to your question as well: Why did Buddha put so much emphasis on no-self?

Combining the different forms of wisdom is an iterative process of knowledge, and they are not mutually exclusive.

Also - to elaborate - we have different proclivities (anusaya), and Buddhaghosa even defined different personality types (caritas) that tends to favor a certain "temperament" over others:

1. greedy temperament [rāga-carita]
2. hateful temperament [doṣa-carita]
3. dull temperament [moha-carita]
4. devout temperament [śraddhā-carita]
5. intellectual temperament [buddhi-carita]
6. discursive temperament [vitarka-carita]

https://www.wisdomlib.org/definition/carita

Depending on what specific tendencies a person may have, there are recommendations on how to proceed in ones practice.

To sum up: We may have to go outside of our natural habits to create a balance that aids us in our practice.

Appropriate attention can and should imo be explained as directing the mind, ie

"There is the case where a monk has some work to do. The thought occurs to him: 'I will have to do this work. But when I have done this work, my body will be tired. Why don't I lie down?' So he lies down. He doesn't make an effort for the attaining of the as-yet-unattained, the reaching of the as-yet-unreached, the realization of the as-yet-unrealized. This is the first grounds for laziness.

There arises listlessness, lassitude, lazy stretching of the body, drowsiness after meals, mental sluggishness; frequently giving unwise attention to it — this is the nourishment for the arising of sloth and torpor that have not yet arisen and for the increase and strengthening of sloth and torpor that have already arisen.— SN 46:51

Instead;

"There is the case where a monk has some work to do. The thought occurs to him: 'I will have to do this work. But when I am doing this work, it will not be easy to attend to the Buddha's message. Why don't I make an effort beforehand for the attaining of the as-yet-unattained, the reaching of the as-yet-unreached, the realization of the as-yet-unrealized?' So he makes an effort for the attaining of the as-yet-unattained, the reaching of the as-yet-unreached, the realization of the as-yet-unrealized. This is the first grounds for the arousal of energy.

Thus one appropriately attends to the arousal of energy instead of arousal of laziness.

There is the element of rousing one's energy, the element of exertion, the element of continuous exertion; frequently giving wise attention to it — this is the denourishing of the arising of sloth and torpor that have not yet arisen and of the increase and strengthening of sloth and torpor that have already arisen.— SN 46:51

That is appropriate attention because one such as this attends properly to the aggregates and recognizes the path.So one attends to and grasps properly the aggregates;

“He attends wisely: ‘This is suffering’; he attends wisely: ‘This is the origin of suffering’; he attends wisely: ‘This is the cessation of suffering’; he attends wisely: ‘This is the way leading to the cessation of suffering.’

As in understand it, appropriate attention is the correct assesment of what is and thus knowing the correct course of action. It is the not misapprehending what is going on, the goal, the senses & what the senses present to avoid this;

“This is how he attends unwisely: ‘Was I in the past? Was I not in the past? What was I in the past? How was I in the past? Having been what, what did I become in the past? Shall I be in the future? Shall I not be in the future? What shall I be in the future? How shall I be in the future? Having been what, what shall I become in the future?’ Or else he is inwardly perplexed about the present thus: ‘Am I? Am I not? What am I? How am I? Where has this being come from? Where will it go?’

8“When he attends unwisely in this way, one of six views arises in him. The view ‘self exists for me’ arises in him as true and established; or the view ‘no self exists for me’ arises in him as true and established; or the view ‘I perceive self with self’ arises in him as true and established; or the view ‘I perceive not-self with self’ arises in him as true and established; or the view ‘I perceive self with not-self’ arises in him as true and established; or else he has some such view as this: ‘It is this self of mine that speaks and feels and experiences here and there the result of good and bad actions; but this self of mine is permanent, everlasting, eternal, not subject to change, and it will endure as long as eternity.’

Appropriate attention is to be seen as food for factors of awakening. Inappropriate attention as food for hindrances. That is the scope of these principles afaik.

In short i think that thinking in and by itself is the breaking into speech due to initial application and sustained attention, appropriate attention is then the application of mind associated with enlightenment factors.

One who understands the Dhamma correctly would be moved to meditate as if turban was on fire.

If one keeps thinking about the Dhamma and is not moved to practice then one either has not come to agreement with the Dhamma or simply neglects contemplation which rouses effort.

One such as this will be with hindrances and if he gives appropriate attention it is clearly not enough of it.