To close the loop on our discussion.
I received the Zyxel AX7501 from init7 today (it's cheaper than on Galaxus). It worked out of the box as a router after plugging it in, adding DHCP Option 60 (which wasn't set in the default configuration) and simply visiting swisscom.ch/start.
Then I put it in bridge mode and set DHCP Option 60 on the Mikrotik corresponding DHCP client on the Ethernet interface it was connected to. Everything worked fine after visiting again swisscom.ch/start. No need to set VLAN 10, because it's actually set on the Zyxel in the bridge settings already.
Thanks so much everyone for your help!