Cypress get href attribute

Solution 1: invoke("attr", "href")

Navigate to the URL specified in the element's href attribute:

cy.get(selector)
      .invoke('attr', 'href')
      .then(href => {
        cy.visit(href);
      });

Reference: https://docs.cypress.io/api/commands/invoke.html#Function-with-Arguments

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Solution 2: Prevent content from opening in a new tab.

Remove the target attribute from the anchor element, then click on it to navigate to its URL within the same tab:

cy.get(selector).invoke('removeAttr', 'target').click()

Reference: https://docs.cypress.io/examples/examples/recipes.html#Tab-Handling-and-Links

The code below should do what you're trying to achieve. There is also an entire recipe with suggestions on how to test links that open in new tabs.

it('Advertise link should refer to Contact page', () => {
   cy.get('div.footer-nav > ul > li:nth-child(2) > a')
     .should('have.attr', 'href').and('include', 'contact')
     .then((href) => {
       cy.visit(href)
     })
})

I would also suggest reading through the Cypress document on the best ways to assign and work with variables: https://on.cypress.io/variables-and-aliases