I have not spent a day in law school, so take my advice with that caveat.
As long as you are not recording a tenant in their unit (or have the camera aimed at their window to look inside, for instance), then I think you are fine. There is no expectation of privacy in common areas or outside on the premises.
However, I am reading between the lines here and it seems like the tenant is the real issue here.
Here's what I would do if I were you (in order):
(1) Issue a notice of termination to this tenant, and make sure you comply with your state statute for doing so. As a self manager, life is too short to put up with this. This is your property and you make the rules! There are plenty of qualified applicants that would appreciate an attentive and responsible lessor. Hopefully they are MTM. If not, hopefully their lease term is coming up soon. In most jurisdictions (besides a few left-leaning pockets), you can terminate (i.e. not renew) a lease for any reason (excepting discrimination based on protected class) or no reason. Do not give them a reason. The less you say, the less fodder you give them to argue with you ad nauseum.
(2) If you are still offering term leases, consider offering MTM henceforth. I have written extensively here in on BP about the benefits of MTM and the liabilities with term leases .
(3) Tighten up your lease language regarding cameras. Here are two excerpts from mine that are germane:
22. SECURITY: We do not provide security services to protect you, others, or property. You must look solely to public law enforcement for such protection. We will not be liable for failure to provide security services or for the criminal or wrongful acts of others. Exterior doors should be locked at all times. We have no duty to you to provide security services or devices other than the duty to provide you with (a) an operable lock on each main swinging entry door of the Rental Unit and (b) operable window locking devices for windows that are designed to be opened. After you take possession of the Rental Unit, we will have no obligation or duty to inspect, test or repair any lock or other security device unless you request us to do so in writing. There should be no expectation of privacy in the common areas of the Premises. We reserve the right to place security cameras in those locations at our sole discretion as we deem necessary. Any cautionary measures that we take (whether applicant screening, security cameras, security devices or courtesy patrol services) which may presently exist or later be installed on the Premises are neither a guarantee nor warranty against criminal acts of others on the Premises or otherwise. Your personal safety and security are your personal responsibility. If criminal activity occurs, you should contact the appropriate law enforcement agency.
AND
(n) Cameras may not be placed by you (or at your direction) in common areas or anywhere on the outside of your Rental Unit. Doorbell cameras are permitted on your exterior door(s).
Lastly, regarding the concern about audio recording and its legality, if you find it is not legal in your area, then just disable the audio portion of the recording via the app. It should be just a toggle on the UI. But...as I stated...your REAL problem is (1), above. These other things are red herrings; you are spending time on managing the effect, rather than dealing directly with the cause.
Good luck!