So per that article Duffy thinks he already has the authority to extend the mandatory retirement age...
The Secretary does have that authority. It is clearly denoted at 5 USC 8425(a). And the President can also do it under 5 USC 8425(e). That said, exemptions from the mandatory retirement age can be given... but that doesn't mean one needs to accept an exemption. If you want to go when eligible, or when mandated, then go. I do not believe they can force you to stay if you want to retire and are eligible.
Federal Law: 5 U.S. Code § 8425 - Mandatory separation
(a) An air traffic controller who is otherwise eligible for immediate retirement under section 8412(e) shall be separated from the service on the last day of the month in which that air traffic controller becomes 56 years of age or completes 20 years of service if then over that age.
The Secretary, under such regulations as the Secretary may prescribe, may exempt a controller having exceptional skills and experience as a controller from the automatic separation provisions of this subsection until that controller becomes 61 years of age. The Secretary shall notify the controller in writing of the date of separation at least 60 days before that date. Action to separate the controller is not effective, without the consent of the controller, until the last day of the month in which the 60-day notice expires. For purposes of this subsection, the term “air traffic controller” or “controller” has the meaning given to it under section 8401(35)(A).
..........
(e) The President, by Executive order, may exempt an employee (other than a member of the Capitol Police or Supreme Court Police) from automatic separation under this section if the President determines the public interest so requires.
..........
The regulation permitting this is clearly denoted at 5 CFR 842.806(b).
Federal Regulation: 5 Code of Federal Regulations § 842.806 Mandatory separation.
(b) Exemptions from mandatory separation are subject to the conditions set forth under 5 U.S.C. 8425.
An exemption may be granted at the sole discretion of the head of the employing agency or by the President in accordance with 5 U.S.C. 8425(c). (Note: It says the President can do this under 8425(c), but that is now 8425(e) as noted above.)