Herewith two options:

• TLDR:
  If you want to use Single Server Private Network, then I would suggest download and use xcp-ng/xenadmin:
  https://github.com/xcp-ng/xenadmin/releases
• You prefer XOA? Well then read on.

As they say: YMMV

In my experience the private network settings process in XOA is broken.

Try the following:

• XO->Settings->Plugins
  Ensure the sdn-controller is enabled.
  If you are lucky enough it may enable.

Chances are if you have the newer XOA, it may fail with:
plugin.load
{
"id": "sdn-controller"
}
{
"code": 10,
"data": {},
"message": "plugin not configured",
"name": "XoError",
"stack": "XoError: plugin not configured
at invalidParameters (/opt/xo/xo-builds/xen-orchestra-202208251357/packages/xo-common/api-errors.js:26:11)
at default.loadPlugin (file:///opt/xo/xo-builds/xen-orchestra-202208251357/packages/xo-server/src/xo-mixins/plugins.mjs:210:13)
at Xo.call (file:///opt/xo/xo-builds/xen-orchestra-202208251357/packages/xo-server/src/api/plugin.mjs:61:14)
at Api.#callApiMethod (file:///opt/xo/xo-builds/xen-orchestra-202208251357/packages/xo-server/src/xo-mixins/api.mjs:306:33)"
}

If you don't have the above issue, you can try and enable a private network, however the network created always seems associated to one of the NIC's and has PIV: tunnel0/1/x. This may not be want you want, but it does work correctly (it seems one can ignore the warnings).

When I state "newer", in this build:

• Xen Orchestra, commit 1297c
• xo-server:5.100.1
• xo-web 5.101.1
  The private network is grayed out, and enabling the sdn-controller fails.

I have an older Xen Orchestra, with caveats noted above, that does work:
When I state "older", this build:

• Xen Orchestra, commit 1dad6
• xo-server:5.87.0
• xo-web 5.92.0

The above are deployed on xcp-ng 8.2, with the effects noted above.

However with xcp-ng/xenadmin all works correctly as expected.

So if anyone has read this far, then hopefully you understand why my feeling is that xcp-ng/xenadmin may be the better solution for this aspect of network administration.

Constructive suggestions welcome.