I found Github project that implements Interstellar-style wormholes in WebGL, with some demos: https://sirxemic.github.io/Interstellar/ and https://sirxemic.github.io/wormhole/
Perhaps @INovaeFlavien can use these as examples and/or sources of inspiration a “real warp/wormholes” effect?
I particularly like the first link, where the wormhole is like a “spherical portal”, that is, without a “tunnel”. You can move sideways, be partially in one place, and partially in another.