State between Equanimity and 1st or 2nd or further path

There are 16 steps to Anapanasati meditation. And almost all of us are at the first two to four steps. If one has a good foundation in virtue or morality (sila), a good knowledge of the Dhamma, and has established a solid base for developing the fourfold mindfulness, one will not get caught in any of the trappings.

What you have mentioned is "Experiencing the Highly Concentrated Mind (Step 10)" of the Ananda Sutta (SN 12:10):

Citta patisamvedi assasissami’ti sikkhati.
Citta patisamvedi passasissami’ti sikkhati

First he trains himself to breathe in sensitive to pleasure, and to breathe out sensitive to pleasure. Now what is he developing successively? Equanimity – the result of a calm concentrated mind. At this we get attached to that pleasure in mind. But if one can cognize all differences that occurre in mind – then one can experience the mental formations – feeling and perception in anapanasati, without being swayed by them. Then one is very sensitive to the mind. Experiencing the highly concentrated mind that is inclined to equanimity, one breathes in and breathes out, in training oneself.

"equanimity of formation" is the 11th stage of insight knowledge(out of sixteenth stages) where all phenomenon one can make notice definitely and may feel like enlightened. If you understand it is not the goal, keep on your mindfulness and your notice on all the phenomenon become faster and clearer and come to a sudden end just like a candle light went out or just like you cut out a tiny string of rope with a sharp knife this phenomenon cannot be described by words. Sharp mindfulness is important to go through this phase and also your entire faith in your meditation master is also important that is you are going the right way.

What is being asked about in the question is from Vipassana Dhura, which is 16 stages of insight from the Visuddhimagga, written by the commentator Buddhaghosa in 430 CE in Sri Lanka.

The sequence of the 16 stages of Vipassana Dhura is not something the Buddha taught & can be confusing because terms used in Vipassana Dhura that indicate a beginning stage of insight- such as 'nibbida' - the Buddha used as the final stage of insight (eg. SN 12.23 - 'disenchantment'). This can make discussions about Vipassana Dhura difficult.

That said, some degree of 'nibidda' (disenchantment with worldly things) is required at the beginning of the path. Therefore, the stages in Vipassana Dhura do have some validity.

The teachings attributed to the Buddha describe the following kind of 'equinimity' (which is called 'Sense Restraint') before the arising of the path:

On seeing a form with the eye, he doesn't grasp at any theme or details by which — if he were to dwell without restraint over the faculty of the eye — evil, unskillful qualities such as greed or distress might assail him. On hearing a sound with the ear... On smelling an aroma with the nose... On tasting a flavor with the tongue... On touching a tactile sensation with the body... On cognizing an idea with the intellect, he doesn't grasp at any theme or details by which — if he were to dwell without restraint over the faculty of the intellect — evil, unskillful qualities such as greed or distress might assail him. Endowed with this noble restraint over the sense faculties, he is inwardly sensitive to the pleasure of being blameless.

MN 38

This 'equinimity' of not grasping at 'themes', when well developed, can become a kind of (deluded) liberation, described in the scriptures (MN 43 called 'theme-less awareness-release').

This 'equinimity' can be a state of delusion because the mind, being accustomed to the feeling of liberation via 'non-judging' or 'non-discrimination', does not discern the characteristics & cause-&-effect realities of many things.

This kind of 'equinimity' many Hindu, Mahayana & Zen traditions call 'advaita' or 'non-duality'. It is a delusion because the mind believes 'non-thinking' & 'non-discrimination' is liberation. Thus, the mind clings to 'non-thinking'; not clearly seeing thinking (sankhara khandha) is also 'not-self'.

Even some Theravada Sri Lankans, such as Katukurunde Nyanananda, give the impression of this delusion, as they give the impression they believe the ending of thinking ('sankhara') is Nibbana.

It should be noted this 'equinimity' is not the equinimity of the 4th jhana because the stream-enterer (1st path) has not reached the 4th jhana.