Why the Buddha abandoned asceticism

Didn't the Bodhisattva master the Jhanas with teachers before his remembering about Jhana states as a child while practicing extreme asceticism? What am I missing here?

The Middle Way is not eating extremely well and it is not eating extremely little. The middle way is in the middle of those two extremes so the Buddha was a mild ascetic or middle way ascetic.

In MN 36:33 (i 247) the Buddha says: "I considered, 'It is not easy to attain that pleasure with a body so excessively emaciated. Suppose I ate some solid food - some boiled rice and porridge.'" (Nanamoli and Bodhi, Middle Length Discourses of the Buddha, p. 340). What is especially interesting here is that the Buddha explicitly identifies the practice of the path with the experience of wholesome pleasure, as against the pain of his previous asceticism.

here's a precise link to relevant portion of the MN 36

https://suttacentral.net/en/mn36/36-42

the discovery of the middle way is not only manifested in the decision to resume eating and stop tormenting the body because austerities impede entering the jhana, but primarily in my opinion in the actual realization that the pleasure of jhanas is permissible and desirable because it's not sensual, only then came the understanding of incompatibility of severe asceticism with jhanas

this positions the Dhamma halfway between the practices of ascetics who avoided any kind of pleasure, being of the opinion that pleasure in future lives, or even liberation, is secured with suffering in this life (like the jains), and indulgence in low carnal sensuality

Maybe MN 26 is more relevant: towards the end of it, the Five ask questions like,

When this was said, the group of five monks replied to me, 'By that practice, that conduct, that performance of austerities you did not attain any superior human states, any distinction in knowledge & vision worthy of a noble one. So how can you now — living luxuriously, straying from your exertion, backsliding into abundance — have attained any superior human states, any distinction in knowledge & vision worthy of a noble one?'

... and afterwards, the end of the sutta is of their being taught the various jhanas.

There may be somewhere where it's stated as a positive, i.e. "eating well was necessary to pursue the jhānas and the Middle Way" -- I think I've read something like that, but I don't remember whether that's a direct quote or an indirect paraphrase.

The only versions I've found at the moment are expressed as a double-negative, not as a positive, i.e. that "utmost austerity is not the way"; for example from this translation of the (non-canonical) Introduction to the Jâtaka,

And the Future Buddha, thinking, "I will carry austerity to the uttermost," tried various plans, such as living on one sesamum seed or on one grain of rice a day, and even ceased taking nourishment altogether, and moreover rebuffed the gods when they came and attempted to infuse nourishment through the pores of his skin. By this lack of nourishment. his body became emaciated to the last degree, and lost its golden color, and became black, and his thirty-two physical characteristics as a great being became obscured. Now, one day, as he was deep in a trance of suppressed breathing, he was attacked by violent pains, and fell senseless to the ground, at one end of his walking-place.

...

Now the six years which the Great Being thus spent in austerities were like time spent in endeavoring to tie the air into knots. And coming to the decision, "These austerities are not the way to enlightenment," he went begging through villages and market-towns for ordinary material food, and lived upon it. And his thirty-two physical characteristics as a great being again appeared, and the color of his body became like unto gold.

Then the band of five priests thought, "It is now six years that this man has been performing austerities without being able to attain to omniscience. And how much less can he be expected to do so in future, now that he has again taken to ordinary material food begged from town to town! He has become luxurious, and given up the Struggle. For us to look for any benefit to come from that quarter would be as reasonable as if a man were to imagine he could bathe his head in a dew-drop. We will have nothing more to do with him." With that they took their bowls and robes, and left the Great Being, and going eighteen leagues off, entered Isipatana.

There are suttas which describe or recommend an attitude towards food (I expect there are in the vinaya too), for example from the Bhikkhuni Sutta,

'This body, sister, comes into being through food. And yet it is by relying on food that food is to be abandoned.' Thus was it said. And in reference to what was it said? There is the case, sister, where a monk, considering it thoughtfully, takes food — not playfully, nor for intoxication, nor for putting on bulk, nor for beautification — but simply for the survival & continuance of this body, for ending its afflictions, for the support of the holy life, [thinking,] 'Thus will I destroy old feelings [of hunger] and not create new feelings [from overeating]. I will maintain myself, be blameless, & live in comfort.' Then he eventually abandons food, having relied on food. 'This body, sister, comes into being through food. And yet it is by relying on food that food is to be abandoned.' Thus was it said, and in reference to this was it said.