When using Chrome in Android, it may bypass the DNS settings set in the
Wireguard configuration. In my case, this happened only when on mobile
networks, not on Wifi, for some reason. When in mainland China, this means
e.g. that Google can't be accessed in Chrome. (Firefox worked fine for me)

To fix this, go to chrome://flags and search for "DNS" in the search field.
Change the setting of "Async DNS resolver" to "Disabled".

Cheers,
Kai