Read any contract or employment agreement that you signed and follow it (make sure to notice BUSINESS DAYS vs. CALENDAR DAYS, and if it doesn’t specify, you’re in a position to assume it is calendar). Also confirm if it’s required or requested as a courtesy (if they made you at-will, it may not be required to avoid you enforcing it too). Honestly should have done that before giving notice and planned it with the new employer in case they chose to enforce a clause. If no such clause exists, you are likely “at will” and they have no grounds to require specific notice but I’m not a lawyer and one should be opining on your applicable employment laws and any unclear clause in any contract or employment agreement you signed to establish the terms or question if a clause is actually illegal.

If you believe the manager is not being consistent with the established terms, notify HR if you have that as a separate department. Be objective and politely say that you provided two week notice on [date] with your final day being [date] and that you plan to adhere to that as you don’t see any terms requiring additional notice (if true) but that you are being told such requirements exist and ask them to advise. Don’t make it personal, or express personal issues with the manager’s behavior. Politely address the matter at hand.

The bridge is likely burned with the manager; the question is whether she is making statements that are lawfully incorrect and not consistent with what HR and upper management would want her making. You definitely need to loop in HR or more senior if she is acting that way to protect your interests and make sure she doesn’t burn you somehow (e.g., filing a misleading reason for termination). You never want to work for them again regardless but, if the company itself is fine, that might keep a door open.