"Everything will evaporate" is the press-release title, and does not fairly capture the Schwarzschild-black-hole-focused work in the paper press-released by the university. The PR title overemphasizes and mischaracterizes the last paragraph of the paper's conclusion as something more than an appeal for further investigation of central masses other than black holes. Their analysis does not rely on the presence of a (particular family of) horizons (cf. Visser Phys. Rev. D 90, 127502 (2014)), and therefore other spherically symmetric non-rotating central masses (possibly even noncompact ones) might induce this gravitational analogue of the Schwinger effect.
> assumes ... ever-expanding universe
No it does not.
I already gave the link to the preprint in your parent comment, but for ease of access <https://arxiv.org/abs/2305.18521>. Equation (5) therein is the line element, standard Schwarzschild, and in particular you'll notice a lack of \Lambda or any other expansion term. I drew explicit attention to the asymptotic flatness and Israel-Darmois junction conditions in my comment you replied to.
We can "knit" (using junction conditions) an asymptotically flat solution into a cyclical spacetime like the Gorkavyi model in your set of links. Because the re-collapse timescales there are a lot shorter than the black hole era of the standard model, large black holes may not even stop accreting, but they will however still induce the gravitational pair production that is the topic of the paper. This seems at first glance to be comparable to the outgoing gravitational radiation induced by compact objects that Gorkavyi considers. If one takes the gravitational backreaction of the gravitational pair production idea into account, the incoming gravitational radiation might even make it and Gorkayvi roughly compatible (the idea being that it would induce a small acceleration on the BH similar to the "anti-gravity" idea raised in the appendix of his Astro. Bull. 76, 229-247, 2021 paper, contributing to the "Big Bounce"). A generalization of the Vaidya metric seems like it might be helpful. One might even wonder if there could be a gravitational analogue of the Stark effect induced upon close binaries (esp. with his relict neutron stars with large mass ratios) in a Gorkavyi cyclical model.
Unfortunately, since you engage with the title at the top and practically nothing else, you missed an opportunity for taking this type of synthesis seriously.