The samesite = None does not maintain sessions in iframes

Question

i made spring boot webapp(i'll call this A)

i try display A's page on iframe at different site(i'll call this B)

but session is validate after redirect in B's iframe.

i use Spring Security to setting SameSite=None.

like this.

@EnableWebSecurity
public class SecurityConfig extends WebSecurityConfigurerAdapter {
     @Override
     protected void configure(HttpSecurity http) throws Exception {
         http.headers().frameOptions().disable(); // X-Frame-Options
         
         //http.csrf().csrfTokenRepository(csrfTokenRepository());
         
         http
            .csrf().disable()
            .authorizeRequests()
            .antMatchers("/**").permitAll()
            .anyRequest().authenticated();
         
     http.addFilterAfter(new TestFilter(), BasicAuthenticationFilter.class);
    }   
}

public class TestFilter implements Filter {
    public void doFilter(ServletRequest request, ServletResponse response, FilterChain chain) {
        try {
            HttpServletResponse objRes = (HttpServletResponse) response;
            objRes.setHeader("Set-Cookie", "Secure: SameSite=None");
            chain.doFilter(request, objRes);
        } catch(Exception e) {
            throw new RuntimeException(e.getMessage(), e);
        }           
    }
}

but Still not working in B's iframe.

actually, browser shows multiple Set-Cookie in response header.

enter image description here

B's page Use the form tag to send a post request to an iframe.

like this.

    <button onclick="postFrame()">send post to iframe</button>
    <form id="postForm" name="postForm" target="postFrame" method="POST" action="A's url/login">
        <input type="hidden" name="value0" value="foo" />
        <input type="hidden" name="value1" value="bar" />
    </form>

    <iframe id="postFrame" name="postFrame"></iframe>

function postFrame() {   
    document.okcallForm.action = "A's url/login";
    document.okcallForm.submit();
}

A's controller part.

    @RequestMapping("/login")
    public String okcallIframeLogin(HttpServletRequest request, RedirectAttributes  model) throws Exception {
        //check password etc...
        return "redirect:/main";
    }

I want the session to be maintained when redirected from B's iframe.