No CAPsMAN connection over wireless backhaul (hAP ax3 + wAP ax)

I would say that the thingies are called CAP and CAPSMAN for a reason, and they are not called CSTATION and CSTATIONSMAN.

Stations (clients) are not configured through CAPSMAN, AFAICT.

But the radio set as AP should be able to reach the CAPSMAN and get the settings from it.

Besides and before the issues (if any) with VLAN(s) you should get rid of the asterisks in your configuration, see point #21 here:

You have one in dhcp client interface (that is probably irrelevant) but you have also one on the wifi1 datapath (that may be well the key issue).

And consider that right now you have set the wAP as "station", while most likely you want it set as "station-bridge", see: