Cookie set with cy.request (set-cookie response) on http local domain is not sent after a 302 redirect on this domain

[Lexa-tech]

Current behavior

Hello, I tried to find a related issue before posting but I couldn't find the exact situation.
I use cy.request to send a login request (POST http://local.domain/login) that set a cookie in the response header set-cookie.
If I visit the page http://local.domain/index.html to the same domain, the cookie is sent in the request headers and I am logged to the application.
Then, I use a third party website to log in and get an accesstoken, but when this third part site redirected me to the application with an 302 HTTP redirect (toward http://local.domain/index.html), the cookie is not used.
I see that the cookie is filtered in the debug tools, certainly due to a same-site constraint, but I don't know why this is happening only with the 302 redirect.
If you have any ideas.
This is working with https://local.domain (but we have some constraints to use http).
This is working if I log in using the prompt login/password in ny application (end to end actions), so it seems that cy.request sets a cookie for the browser that cannot be reused with a 302 redirect in HTTP local url
Thanks.

Desired behavior

Cypress should be able to reuse the cookie whith redirect 302, like Cypress does when navigating to the page with a cy.visit.

Test code to reproduce

cy.request http://local.domain/login => cookie is set OK
navigation to the page with cy.visit http://local.domain/index.html => OK, the page is loaded and cookie is sent in request header
SSO login process to a third part app , redirect 302 => error when returning to the page http://local.domain/index.html => cookie is not sent (filtered) and the return to the app is KO

This is the JSESSSIONID cookie when redirected to index.html

Cypress Version

13.8.0

Node version

18.9.0

Operating System

Windows

Debug Logs

No response

Other

No response