I hope this message finds you well, present circumstances excluded. The answer to this question is somewhat complicated, as you can imagine. Both New York and Florida are members of an agreement which is called the Driver License Compact (DLC). This DLC means that signatory states will honor the decisions of other states in the compact relative to driver license issues. However, each state will apply their own law to the particular infraction.
An example would be that a person gets a DUI in Florida and has an Alabama license. DUI in Florida, hypothetically is a 6 month license suspension and it is only 3 in Alabama. The person's license in Alabama will only be suspended for 3 months by the licensing state of Alabama under the compact even though the infraction took place in FL.
In your case, New York will apply its own law relative to mandated driver's test and suspensions for failure to appear. New York does not have a law which suspends a person's license for failure to appear for a road test. As such, you New York license should not be suspended, despite what FL is telling you. However, if you were pulled over while driving in FL, they could cite you for driving on a suspended license in their state because they have revoked your privileges in their state.
In short, your New York license should not be suspended in view of the Driver License Compact, but you cannot drive in Florida because they will not recognize your license as valid based on their own suspension of your license or revocation of your privileges to drive in Florida.
Let me know if you have any additional questions or comments.
Best wishes going forward!