I've managed to get this working. There were two issues, first of all, the AuthenticationType gets "Umbraco." prepended, which then fails in BackOfficeController, because AuthenticationType is now "Umbraco.https://localhost:12345", while LoginProvider is still "https://localhost:12345"

var authType = OwinContext.Authentication.GetExternalAuthenticationTypes().FirstOrDefault(x => x.AuthenticationType == loginInfo.Login.LoginProvider);
if (authType == null)
{
    Logger.Warn<BackOfficeController>("Could not find external authentication provider registered: " + loginInfo.Login.LoginProvider);
    return false;
}

What prepends the "Umbraco." bit is done in

idAuth.ForUmbracoBackOffice("btn-google-plus", "fa-google-plus");

, but adding the lower bit, after calling the upper method fixed the issue.

idAuth.AuthenticationType = "https://localhost:12345";

2nd problem was the null value of loginInfo.ExternalIdentity.Name, which was taken from ClaimsIdentity.Name (which was null itself).

var autoLinkUser = new BackOfficeIdentityUser()
{
    Email = loginInfo.Email,
    Name = loginInfo.ExternalIdentity.Name,
    UserTypeAlias = userType.Alias,
    AllowedSections = autoLinkOptions.GetDefaultAllowedSections(UmbracoContext, loginInfo),
    Culture = autoLinkOptions.GetDefaultCulture(UmbracoContext, loginInfo),
    UserName = loginInfo.Email
};

By claims transforming I now have a proper ClaimsIdentity object, with Name filled in:

var idAuth = new OpenIdConnectAuthenticationOptions();
idAuth.Notifications = new OpenIdConnectAuthenticationNotifications
{
    SecurityTokenValidated = async n =>
        {
            var id = n.AuthenticationTicket.Identity;

            // we want to keep first name, last name, subject and roles
            var givenName = id.FindFirst(System.Security.Claims.ClaimTypes.GivenName);
            var familyName = id.FindFirst(System.Security.Claims.ClaimTypes.Surname);
            var roles = id.FindAll(System.Security.Claims.ClaimTypes.Role);

            // create new identity and set name and role claim type
            var nid = new ClaimsIdentity(
                id.AuthenticationType,
                System.Security.Claims.ClaimTypes.GivenName,
                System.Security.Claims.ClaimTypes.Role);

            nid.AddClaim(givenName);
            nid.AddClaim(familyName);
            nid.AddClaims(roles);
            nid.AddClaim(id.FindFirst(System.Security.Claims.ClaimTypes.NameIdentifier));
            nid.AddClaim(id.FindFirst(System.Security.Claims.ClaimTypes.Email));

            n.AuthenticationTicket = new AuthenticationTicket(
                nid,
                n.AuthenticationTicket.Properties);
        }
};