cy.url() and/or cy.location('href') does not return a string

tl;dr

Cypress commands are asynchronous, you have to use then to work with their yields.

cy.url().then(url => {
  cy.get('.editor-toolbar-actions-save').click();
  cy.url().should('not.eq', url);
});

Explanation

A similar question was asked on GitHub, and the official document on aliases explains this phenomenon in great detail:

You cannot assign or work with the return values of any Cypress command. Commands are enqueued and run asynchronously.

The solution is shown too:

To access what each Cypress command yields you use .then().

cy.get('button').then(($btn) => {
  // $btn is the object that the previous
  // command yielded us
})

It is also a good idea to check out the core concepts docs's section on asynchronicity.

These commands return a chainable type, not primitive values like strings, so assigning them to variables will require further action to 'extract' the string.

In order to get the url string, you need to do

cy.url().then(urlString => //do whatever)