What happens, when you reload this page https://www.whatsmyip.org/ ?
But when I look at the firewall -> live view of both wireguard interfaces, I see traffic on one WG interface only and on the other one it's just every now and then some ICMP and that's all, what am I missing?
Are you testing multiple LAN clients? It would be very bad for your Internet experience if requests from a single machine would alternatingly use both tunnels.
Unless you have e.g. 10 clients and can check if on average 5 are using each tunnel, testing is difficult in such scenarios. What are you trying to achieve? You have a single Internet uplink or two?
I see a page with lots of info, starting from my IP address, and username & user agent, etc. - I can't take a screenshot as I'm testing that with the browser of my TV (which is connected via Wireguard)...