After further testing AP Manager, I came to realize that as long as FAPs are centrally managed by AP Manager, the WiFi Profiles I can configure at AP Manager seems to be saved in Policy&Objects' CLI Only Objects section under wireless-controller->wtp-profile. When I changed it at AP Manager, the same change shows up in CLI Only Objects.
And when I change it at CLI Only Objects, it shows at AP Manager.
The problem now is it doesn't seem to be consistent. While I was testing above by change country from US to CA, and CA back to US, installation attempt failed due to:
error -2 - channel 165 is not supported. dfs=yes,region=,plat=221E,cnty=US,band=802.11ac,bond=40MHz
Also when I changed it via CLI script (changed a different part of profile), it didn't recognize the change to be installed.
I think this is a bug(s) at least with 6.4.8 we use instead this operation was not intended. But for now, we'll skip AP Manager feature and stick to CLI template(s) + meta field, which is very consistent.