Intercept the general pattern for the avatars, find out which specific avatar from the URL then apply the fixture dynamically.

Since you control the mocks in /images you don't need base64.

cy.intercept('**/avatars/default/*', (req) => {
  const img = req.url.split('/').at(-1)
  req.reply({
    fixture: `../../images/${img}`
  })
})