cy.intercept not applying header

I'm using cypress to test an api, and I've got an access_token parameter in the hash that I need to stick in the Authorization header for all requests.

In the example below, if I use the header directly in the request() call, everything works perfectly. If I move it into the interceptor, I get a 401/Unauthorized. What am I doing wrong?

cy.location('hash').then((hash) => {
    // Extract access_token from hash
    const params = new URLSearchParams(hash.replace('#', ''));
    const accessToken = params.get('access_token');
    cy.log(`Adding Authorization header: Bearer ${accessToken}`);

    // Intercept all requests
    cy.intercept('*', (req) => {
      // Add Authorization header
      
      if (accessToken) {
        //req.headers['Authorization'] = `Bearer ${accessToken}`
      }
      req.continue()
    }).as('auth');

    cy.request({
      url: '/v1/me',
      method: 'GET',
      headers: {
        'Authorization': `Bearer ${accessToken}`
      }
    }).then((response) => {
      expect(response.status).to.eq(200)
      expect(response.body).to.have.property('email')
    })
  });

Seems like cy.request isn't intercepted by cy.intercept, which makes close to zero sense, but you can wrap fetch up, which IS handled by:

cy.wrap(null).then(async () => {
  const response = await fetch('/v1/me')
  const data = await response.json()
  expect(data).to.have.property('email')
})

The fetch() call will trigger the intercept() call, which you can then use to apply auth headers, etc.