I've installed the package called Sustainsys.Saml2 this comes with a built in way to register it much like the OIDC providers.

However the button simply does not show up on the backoffice login screen, this is my code:

                    backOfficeAuthenticationBuilder.AddSaml2(
                        backOfficeAuthenticationBuilder.SchemeForBackOffice(SamlUserExternalLoginProviderOptions.SchemeName),
                        options =>

                        {
                            options.SignInScheme = CookieAuthenticationDefaults.AuthenticationScheme;
                            options.SPOptions.EntityId = new EntityId("");
                            var identityProvider = new IdentityProvider(new EntityId(""),
                                options.SPOptions)
                            {
                                SingleSignOnServiceUrl = new Uri(""),
                                Binding = Saml2BindingType.HttpRedirect,
                            };
                            identityProvider.SigningKeys.AddConfiguredKey(new X509Certificate2("testcert.cert"));
                            options.IdentityProviders.Add(identityProvider);
                        }
                    );

Pulling my hair out here 😅 It looks like it "should" work