Cypress Login With Redirect

Your code is pretty close, here's what I think you need to change.

Avoiding frame-busting

You should be able to avoid the redirect jumping out of the Cypress runner by visiting it directly inside the cy.session().

Calling pattern for cy.session()

cy.session() should be in a beforeEach() not a before(). It's purpose is to reinstate the auth cookies for each it(), so it must be called before each test.

Visit main URL at the top of each test

cy.visit('https://localhost:3000') is required for every test, see session

Because the page is cleared at the beginning of each test, cy.visit() must be explicitly called at the beginning of each test.

Origin command isn't required

cy.origin() is not required when the two origins are in different execution blocks, i.e https://staging.XXX.com/login in the beforeEach() and https://localhost:3000 in the it() block.

Here is the general pattern, I've left out some lines for clarity

describe('User Session + Start a Discussion', () => {

    beforeEach(() => {
        cy.session("User Session", () => {
            cy.visit('https://staging.XXX.com/login')
            cy.contains('Log In').click()
            ...          
            cy.get('input[placeholder="Username or Email"]').type(username)
            cy.contains('Next').click()
            cy.get('input[placeholder="Password"]').type(password)
            cy.contains('Log In').click()
            ...
        })
    })

    it('Starts a new Discussion', () => {
        cy.visit('https://localhost:3000')       //  logged-in state
        ...
    })

    it('Further test', () => {
        cy.visit('https://localhost:3000')       //  logged-in state
        ...
    })
})

First of all, thank you for your quick and kind reply.

Based on your reply and this vid I updated my code to:

describe('User Session + Start a Discussion', () => {

// Creating User Session
beforeEach(() => {
    cy.session("User Session", () => {
                
        cy.visit('https://localhost:3000/')
        
        cy.contains('Log In')
            .click()
        
        cy.origin('https://staging.XXX.com/', () => {
            cy.contains('Allow All Cookies', { timeout: 60000 })
                .should('be.visible')

            cy.contains('Allow All Cookies')
                .click()

            cy.get('input[placeholder="Username or Email"]')
                .type("USERNAME")
        
            cy.contains('Next')
                .click()
            
            cy.get('input[placeholder="Password"]')
                .type("PASSWORD")
            
            cy.contains('Log In')
                .click()

            cy.get('button[data-bind="html: actionButtonHTML, click: consentToGrantAction, disable: busy"]', { timeout: 120000 })
                .should('be.visible')

            cy.get('button[data-bind="html: actionButtonHTML, click: consentToGrantAction, disable: busy"]')
                .click()
        })

    })
})

// Runs the Discussion test
it('Starts a new Discussion', () => {
    cy.visit('https://localhost:3000/')
    
    cy.get('a[href="/discussions"]')
        .click()

    cy.contains('Start a discussion', { timeout: 10000})
        .click()

    cy.contains('Attach to Discussion...')
        .click()

    cy.get('#object-selector-modal-1').should('be.visible')

    cy.get('[data-classname="file"]')
        .click()

    cy.get(':nth-child(1) > .media > .media-body > label > input')
        .click()
    

    cy.get('[data-bind="click: save, css: {disabled: !canSave()}, disable: !canSave()"]')
        .click()

    cy.get('textarea[class="ace_text-input"]')
        .type("New Discussion", {force: true})

    cy.contains('Publish')
        .click({force: true})

    cy.contains('Publish selected objects')
        .click({force: true})

    cy.pause()
})

})

But I am still facing the problem with jumping out of the Cypress runner as once I click to the Log In button it redirects the user multiple times as shown on the following picture

I am able stay in the Cypress runner and also to log in when I visit directly the login page cy.visit('https://localhost:3000/login') but once the user is authenticated then the URL stays as https://staging.XXX.com/login?redirect_uri=https%3A%2F%2Flocalhost%3A3000%2Freturn_from_login&client_id=CLIENT_ID&scope=%7B%22full%22%3A+true%7D" and not https://localhost:3000/

So my conclusion is that if I would somehow manage to stay in the same window then your suggested code would be working.

Is there something like forceStayInThisTab function or any other idea how to force Cypress to do multiple redirects in the same window?

I checked the code of the Log In button and unfortunately it's not HTML target="_blank" but it's done via JavaScript..