If you're feeling ambitious you can digest Woolsey 2017 https://arxiv.org/abs/1608.08939v2 which is about pulsational pair instability supernovae (PPISNs) and which by coincidence I had on hand because I was reading about LIGO's 50-135 M_{sun} remnant mass gap[1].

The first couple paragraphs of Woolsey 2017 are a good basis for an answer to the question, "what happens to the positrons?", and the answer is that they and the electrons contribute to complicated nuclear fusion chains more centrally within the star.

The central regions in which these gammas are being produced are extremely dense, and maybe it is helpful to think of a piece of some oxygen or silicon nucleus being squeezed in between the e+e- pair such that electron capture "steals" the electron and its part of the gamma's momentum, and the daughter products include neutrinos (which tend to carry momentum right out of the star system, since practically everything in the area is transparent to neutrinos).

In effect, the momentum of a centrally-produced gamma ray radiation kicks inner parts of the star outwards, but when the gamma ray's momentum "condenses" into e+e- pairs, a good fraction of the momentum ends up trapped within denser nuclei, or converted into neutrinos.

The electric charge is very strong so any "excess" positrons will quickly find another electron to annihilate with -- and there are plenty in the star (say, in less-central regions) to meet. The positron will be "pulled" part way up, and prospective partners with the opposite charge will be "pulled" part way down. They're likely to meet somewhere away from the central region, especially if there is a significant positron excess centrally. An annihilation gamma produced much closer to the surface can only lift the surface matter with the gamma's momentum, doing nothing to lift much more next-to-central regions away from the most central regions. Moreover, since the e+e- annihilation gamma can go in any direction, it has a greater chance of pushing less-central regions towards the centre than a nuclear fusion gamma produced very centrally.

Finally, Plait's Bad Astronomy article at the top also links to Plait's earlier https://www.syfy.com/syfywire/the-star-that-blew-up-a-little... which tries to describe PISNs for the readers following the sentence, "What follows is still somewhat hypothetical, but astronomers are working on this problem, and many think this can explain this very odd class of exploding star …"

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[1] There's a lack of observational evidence for black holes in that mass range, and if PPISNs are commonplace that might be why they don't exist, as opposed to other possibilities such as massgap BHs exist but their near-regions don't radiate much compared to the background). In essence PPISNs and PISNs reliably throw away enough mass that ~ 55-133 M_{sun} SN remnants are prohibited, and we can only get compact objects in that massgap through mergers or the like. More here https://arxiv.org/abs/1709.08584 if you're very interested, and the two authors are worth an author-search as they are prolific in this area.

What do you mean? Taking a guess at answering that, electrons and positrons aren't electrically neutral: they are very very strongly attracted to one another, especially compared to

> gravitational collapse

so the probability of electron-positron annihilation immediately after pair production is in general extremely high! (In lab settings you need strong magnetic traps to avoid that.)

The "trick" in the star's core is to remove the electrons locally, or alternatively to convert the mostly-elastic photon-nucleus scattering with a much more inelastic photon-nucleus scattering.

I've described the former in sibling comments -- oxygen and silicon are present in these stellar cores and aggressively capture electrons. The positrons then are pulled outwards by electrons outside the core, and annihilate there. I omitted that an electron-positron annihilation produces two (or more) gammas rather than one, and that the photons can go in (different) arbitrary directions.

The latter is also an important contributor. The gammas in question are not even close to being in free space. They're in a region densely populated by high-atomic-number nuclei, and the Z^2 contribution in https://en.wikipedia.org/wiki/Quantum_mechanical_scattering_... dominates. If the region were all lighter nuclei (hydrogen, helium) the probability of pair production would be much lower.

Roughly speaking, in the absence of immediate electron capture by the nucleus the pair-producing gamma "hits", the momentum of the gamma is split three ways: into each of the electron and positron, and into the nucleus. Electron capture is in effect just an extreme inelastic collision.

In the no-electron-capture case, the heavy nucleus, having absorbed the "recoil" proportion of the gamma into its internal degrees of freedom, has several ways to get rid of that momentum, re-emission of one or more photons with lower energy than the gamma, or transmutation (which might produce neutrinos).

If the electron and positron pair immediately annihilate, they do so minus the "recoil" energy to start with; additionally they produce more than one gamma, and in arbitrary directions. Consequently, there is less momentum available for subsequent elastic collisions.