I just found the solution: just simply enable "Reroute location requests to the OS" (within Settings -> Apps -> Sandboxed Google Play). Now the Dutch website drgl.nl shows the nearby public transport stops based on current location.
It still leaves me with a question: why has the settings of Sandboxed Google Play influence on showing the current location within Vanadium? Vanadium is not linked with Google Play? I don´t know exactly what the rerouting location requests function does. I presume the website asks for Google Play location, but Pixel 8a is set to GrapheneOS as location service. With the rerouting enabled, the website uses in fact GrapheneOS location service instead of Google location service.
It could also explain why the CoMaps app still shows current location while the NS app didn´t. The first is downloaded from Obtainium, the latter from Google Play. Since the rerouting location is enabled, the NS app now shows current location.
Please correct me if I'm wrong.