But even the hybrid wold be considered introduced by iNat definition - it arrived in the region via anthropogenic means. Humans transporting parent and frowing them together in the garden seems pretty anthropogenic to me (not to mention that the first habitats were also anthropogenic).
This means without humans, the species would not even exist. It is similar to horticultural hybrids and cultivars - they are also not native to anywhere.
(the matter is often not so simple, as it is often not clear what influence people had, but for this species, it appears we know exactly what happened, and should be easy to classify it). These matters often raise questeions what exactly is an artificial infulence of humanity? When exactly have stopped being part of nature? Is the current distribution of European tree species native or man-made? It is quite clear many of the were dispersed north and east by early humans, but it is also hard to argue this was an unnatural process
That said,
one nativeness arises from an ecological-evolutionary standpoint (which S. squalidus is not and cannot be), there is also nativeness from a cultural and legal sense (which, if brittish people decide it is, it can be, and gets the legal protections of a native endemic species).