Many suttas (such as SN 45.8, MN 117, MN 27 & AN 10.61) describe the place of mindfulness (sati) & situational awareness (sampajānna) in the Path, where mindfulness & sampajano are established prior to jhana.
MN 117 says:
In one of right mindfulness, right concentration comes into being.
MN 27 says:
When they have this entire spectrum of noble ethics, this noble
contentment, this noble sense restraint, and this noble mindfulness
and situational awareness, they frequent a secluded lodging—a
wilderness, the root of a tree, a hill, a ravine, a mountain cave, a
charnel ground, a forest, the open air, a heap of straw... Giving up
covetousness for the world, they meditate with a heart rid of
covetousness, cleansing the mind of covetousness...They give up these
five hindrances, corruptions of the heart that weaken wisdom.... Then,
quite secluded from sensual pleasures, secluded from unskillful
qualities, they enter and remain in the first absorption...
AN 10.61 says:
Thus associating with good persons, becoming full, fills up hearing the good Dhamma. Hearing the good Dhamma, becoming full, fills up faith. Faith, becoming full, fills up careful attention. Careful attention, becoming full, fills up mindfulness and clear comprehension. Mindfulness and clear comprehension, becoming full, fill up restraint of the sense faculties. Restraint of the sense faculties, becoming full, fills up the three kinds of good conduct. The three kinds of good conduct, becoming full, fill up the four establishments of mindfulness. The four establishments of mindfulness, becoming full, fill up the seven factors of enlightenment. The seven factors of enlightenment [which include samadhi & jhana], becoming full, fill up true knowledge and liberation. Thus there is nutriment for true knowledge and liberation, and in this way they become full.
The seven factors of enlightenment are described in suttas such as SN 46.3 & MN 118.
AN 46.3 says:
Bhikkhus, those bhikkhus who are accomplished in virtue, accomplished
in concentration, accomplished in wisdom, accomplished in liberation,
accomplished in the knowledge and vision of liberation: even the sight
of those bhikkhus is helpful, I say; even listening to them … even
approaching them … even attending on them … even recollecting (anussati) them … even going forth after them is helpful, I say. For what reason?
Because when one has heard the Dhamma from such bhikkhus one dwells
withdrawn by way of two kinds of withdrawal—withdrawal of body and
withdrawal of mind.
“Dwelling thus withdrawn, one recollects (anussarati) that Dhamma and thinks it
over (anuvitakketi). Whenever, bhikkhus, a bhikkhu dwelling thus withdrawn recollects
that Dhamma and thinks it over, on that occasion the enlightenment
factor of mindfulness is aroused by the bhikkhu; on that occasion the
bhikkhu develops the enlightenment factor of mindfulness; on that
occasion the enlightenment factor of mindfulness (sati) comes to fulfilment
by development in the bhikkhu.
Dwelling thus mindfully, he discriminates that Dhamma with wisdom (paññāya), examines it, makes an investigation of it. Whenever, bhikkhus, a bhikkhu dwelling thus mindfully discriminates that Dhamma with wisdom, examines it, makes an investigation of it, on that occasion the enlightenment factor of discrimination of states is aroused by the bhikkhu; on that occasion the bhikkhu develops the enlightenment factor of discrimination of states; on that occasion the enlightenment factor of discrimination of states (dhammavicaya) comes to fulfilment by development in the bhikkhu.
MN 118 says:
Bhikkhus, on whatever occasion a bhikkhu abides contemplating the body
as a body, ardent, fully aware (sampajāno) and mindful (satimā), having put away covetousness and grief for the world—on that occasion unremitting mindfulness is established in him. On whatever occasion unremitting
mindfulness is established in a bhikkhu—on that occasion the
mindfulness enlightenment factor is aroused in him, and he develops
it, and by development, it comes to fulfilment in him.
Abiding thus mindful, he investigates and examines that state with
wisdom (paññāya) and embarks upon a full inquiry into it. On whatever occasion,
abiding thus mindful, a bhikkhu investigates and examines that state
with wisdom and embarks upon a full inquiry into it—on that occasion
the investigation-of-states (dhammavicaya) enlightenment factor is aroused in him,
and he develops it, and by development it comes to fulfilment in him.
About the investigation-of-states (dhammavicaya) enlightenment factor, AN 46.2 adds:
There are, bhikkhus, wholesome and unwholesome states, blameable and
blameless states, inferior and superior states, dark and bright states
with their counterparts: frequently giving careful attention to them
is the nutriment for the arising of the unarisen enlightenment factor
of discrimination of states and for the fulfilment by development of
the arisen enlightenment factor of discrimination of states.
About the 3rd jhana, the suttas say:
And with the fading away of rapture, I entered and remained in the third absorption, where I meditated with equanimity, mindful and aware, personally experiencing the bliss of which the noble ones declare, ‘Equanimous and mindful, one meditates in bliss.’
About wisdom (panna), MN 43 says:
Wisdom (paññā) and consciousness (viññāṇaṁ) — these things are mixed, not separate. And you can never completely dissect them so as to describe the difference between them. For you understand (pajānāti) what you cognize (vijānāti), and you cognize what you understand.
To summarise the conclusions of the quotes above:
Mindfulness recollects past knowledge, such as the Dhamma taught by a teacher (AN 46.3)
Situational awareness (sampajanno) functions to ensure meditation proceeds following the parameters of that Dhamma taught by a teacher. In other words, regardless of the definition of sampajanna, it is clear sampajanna always functions together with mindfulness.
What performs dhamma-vicaya (investigation of phenomena/doctrines) is wisdom (panna). Wisdom (panna) is a direct product of the consciousness of the reality of dhammas. The teachings are clear that panna, here, is not sampajanna, and sampajanna, here, is not wisdom. Sampajanna is a type of wisdom arising from mindfulness (bringing to mind past knowledge/learning). Where as panna, here, is a product of consciousness or direct/present seeing.
It appears obvious dhamma-vicaya (i.e., the development of wisdom about what is blameless, inferior, superior, dark and bright) is occurring in the 2nd, 3rd & 4th jhana, thus, about the 3rd jhana, the suttas say: "experiencing the bliss of which the noble ones declare". Therefore, since dhamma-vicaya is obviously occurring in the 2nd, 3rd & 4th jhana, it appears obvious the terms 'vitakka & vicara' in the 1st jhana do not refer to dhamma-vicaya.