How to store oauth2 passwaord grant in a websession using spring cloud gateway?

Question

I'm using Spring Cloud Gateway as a BFF as described in https://www.baeldung.com/spring-cloud-gateway-bff-oauth2.

I now need to do the same using password grant (resource owner password credentials flow) instead of the authorization code flow and I'm completely lost in the Spring Security jungle :-(.

Looking at the spring security docs about password grants, I managed to call an endpoint and ask for an access token using the following snippet:

@GetMapping("/do-login")
public Mono<String> index(ServerWebExchange exchange) {
    OAuth2AuthorizeRequest authorizeRequest = OAuth2AuthorizeRequest.withClientRegistrationId("keycloak-pwd")
            .principal(new UsernamePasswordAuthenticationToken("frodo", "frodo"))
            .attribute(ServerWebExchange.class.getName(), exchange)
            .build();

    return this.authorizedClientManager.authorize(authorizeRequest)
            .map(OAuth2AuthorizedClient::getAccessToken)
            .thenReturn("index");
}

However, I have no idea what to do with it? How can I create a SecurityContext from the results and make sure this is saved in the web session of my BFF?

I was thinking about a way to wire an AuthenticationWebFilter that converts some request using a ServerFormLoginAuthenticationConverter to an UsernamePasswordAuthenticationToken but basically I'm lost and want to be found :-).

Any clues? Guidance? Anything?

P.S.: I know I shouldn't use password grant and that it's deprecated. But I'm not the one to decide :-( .