I think the term "Arrowverse" is only useful if we use it for shows that are connected to the overall narrative continuity on an ongoing basis, rather than just having a single Crisis cameo. After all, Crisis implicitly established that all live-action DC is part of the multiverse, so that definition is too all-inclusive to be useful. A label is only meaningful if it differentiates one group of things from another. Including everything under the label would make the label redunant.
So, for instance, The Flash (1990) is part of the Arrowverse because they brought back Barry-90 twice and made him integral to two consecutive crossovers. But I disagree with the Arrowverse Wiki's inclusion of Birds of Prey as a core Arrowverse show, because it only got a brief cameo in Crisis and has no narrative connection to the main continuity. I'd also exclude the DCEU, despite the Flash crossover scene, because it's already an established shared continuity with a distinct name of its own, and the crossover was not narratively connected to anything else in the Arrowverse (because it was filmed as an afterthought and grafted in).
As for Stargirl, then, it's not part of the Arrowverse yet because it's only had a brief cameo in a montage at the end of Crisis. But they're already talking about doing a proper crossover, and if they do it once, they'll surely do it more than once. So at that point, it will be part of the Arrowverse.