A couple of things to untangle. First, if you have an existing lease and your roommate gives notice, your lease generally continues with you as the remaining tenant. You don't have to apply for a new apartment. At renewal, the landlord can negotiate new terms, but they can't treat you as a stranger unless they're ending the tenancy for a permitted reason.
For a new occupant, the landlord can require they submit an application and prove income ratio. If your friend's NY employer has her working remote from NJ, it may still be acceptable if the employer is based in New York and her wages are NY-taxed, but management may have its own policy. Ask for the standard in writing.
On the fee: unless your lease has a specific amendment or processing fee, they cannot invent one. They may charge the actual credit report cost only. If management says the new person must hit 40x individually even though your income alone qualifies, ask them to explain in writing. It may be a sign they want to use the same underwriting model as a new joint lease.
You could also suggest she be added as a permitted occupant, not co-tenant. That often weakens the fee argument because you remain fully liable. But some landlords won't allow non-leaseholder occupants with keys.