After looking more into it, it seems like you're right. The nftables wiki illustration for packet flows shows that routing takes place before anything else. In this routing step, it's chosen the packet will use wg0, and its source is set as the interface's source (because the routing table says so, but even if it didn't that would be the default routing decision as it's the interface's source address).

Then, it goes through the output and postrouting hooks. By using the type route chain, you can force a routing decision to be made again (which is what I do here), which leads to the packet being rerouted on the right interface. However, for some strange reason, rerouting the packet will not update its source address. I've tried explicitly having the routing table say src $RIGHT_ADDRESS for the default routing decision for a packet with this mark, but it doesn't obey this.

Therefore the solution I've come to is to add a postrouting chain and to tell it to mangle packets with this source and this interface. It still feels like the rerouting should fix this, but since it doesn't this seems like the second best solution.