Turns out the problem was rather mundane, but I'll post it here in case anyone else has the same issue: My physical sim was years old, and originated from a carrier that was bought by Telia (called Chess). They just let their customers keep the old cards, there was no need to swap. But the phone still registers it as Chess under the network settings, and this is obviously not on the list of supported carriers. I got a fresh esim from Telia for my phone, and after that, the watch instantly let me install the esim via the Watch app.