Allow "HTTP" auth users to have themes applied and modify theme settings

My users are externally authenticated.
When they login the authentication provider is set as follows:

        "authentication_provider": {
            "type": "http",
            "name": "__http__"

However, this means it doesn't apply any previously set theme per user for their experience and does not show any Theme modification settings on the "Edit Profile" page.

If the same users log in directly (username/password at Kibana login page) they are authenticated with:

        "authentication_provider": {
            "type": "basic",
            "name": "basic"

Which applies the correct theme and gives them permission to edit the Theme setting on the "Edit Profile" page.

At its core, this page gives JSON data for "basic" users, but a 404 for "http" users: /internal/security/user_profile?dataPath=avatar%2CuserSettings

This seems to stem from the fact that Elastic doesn't populate the user profile fully for "http" auth.

I realise I can probably resolve this through deep modification of server/authentication/providers/http.ts - but I'm wondering if anyone has any pointers before I dive in?