I did more reading and I found this guide.
I cannot bridge the wlan client and ethernet port, but I can create a relay network between them.
I bridged the zerotier and ethernet interfaces in one network as usual, but I assigned a static unused ip to them.
Then, with luci-proto-relay installed I created a relay network between the wlan network and lan network, and assigned the ip of the wlan network to the relay network.
To maintain ssh access I assigned dropbear to the wlan network and rebooted the device.
This works as I want it to, but the performance of lan-to-zerotier connection is very low, probably because the AR300M16 is underpowered. In any case, I don't need speed, just access.
I think the Gl.Inet software's extender mode used a similar configuration. Probably it didn't work with zerotier before because I tried to bridge the zerotier interface to the wrong network.