Problems with UI authorization in Salesforce

[viktarIncountry]

Previously we used the following solution:
cy.request({ body: { pw: credentials.password, un: credentials.username, }, form: true, log: Cypress.env('isDebugLog'), method: 'POST', url: Cypress.env('salesforceLoginUrl'), })

But after the latest security update, this solution no longer works, since MFA is required.
We tried using this solution:
https://help.salesforce.com/s/articleView?id=000386254&type=1

Authorization succeeds, and we're logged into UI. However, when accessing the page via cy.visit(), we get an error:

The following error originated from your application code, not from Cypress.
Unable to read the Aura token from the response.
This error was thrown by a cross origin page. If you wish to suppress this error you will have to use the cy.origin command to handle the error prior to visiting the page.

Has anyone encountered this problem?