I have a hAP ax³ router and have recently obtained a cAP ax. I would like to use the cAP ax as a Wi-Fi extender and Ethernet bridge. It is within Wi-Fi range of the hAP ax³ but there is no nearby wired Ether net connection.

It is a modest home network with few users and doesn't currently use RADIUS. I have no experience with CAPsMAN.

Is it feasible to use CAPsMAN v2 to configure my network like this? Where do I start?

You have to sacrifice one of the radios on cAP ax to create link between both devices, this can not be done via CAPsMAN, you have to do it manually and then you can control the second, remaining, radio by CAPsMAN

I believe that in recent/latest versions of ROS, the 4 address support/station bridge mode has been implemented:
viewtopic.php?t=180369
but I have not seen complete/reproducible examples on its use.

In any case, probably CapsMan - even if it would work, which is not given - seems to me a complication for just two devices.