How do I find all the frequencies for my local TRACON?
There are sector maps available, and each facility updates them periodically.  They are published.  My understanding is that sectors are joined and separated frequently, even based on the minute to minute workload.
(I have a set of charts showing High, Low Center and tracon sectors. I haven't found a public source for those charts yet.  Here is a set of maps, but I would like to provide direct FAA maps.  https://ivaous.org/academy/index.php/controllers/procedures-and-organization  )

The chart supplement and AFD are good places for common frequencies, however most facilities have additional frequencies.  They might be used for certain events, emergencies, when VIPs are being handled, during extreme congestion and when there are problems with the primary frequencies.  I do not know of a good source for those backup frequencies, which is published.

There are radio reference listings of ATC frequencies, however, they are not always accurate.  While the may show the station frequency assignments, they may not show the true facility usage.

As an example, here is a compilation of Boston Air Route Traffic Control Sectors. https://en.wikipedia.org/wiki/Boston_Air_Route_Traffic_Control_Center#Low_Altitude_Sectors_2

Addendum:  FAA Facility Transmitting Authorization (FTA) would be the document, prepared for each facility, which would list all the frequencies that facility is authorized to use.  The genesis and use of the FTA is covered in this FAA Order: https://www.faa.gov/documentlibrary/media/order/6050_32b_with_chg_1_and_2_incorporated.pdf


  For FAA-owned systems, this number will be the Facility Transmitting
  Author ization (FTA) number assigned by FAA Spectrum Engineering. For
  non-federally-owned systems, this number will be the Federal
  Communications Commission (FCC) license number or “call sign” assigned
  by the FCC.  For military-owned systems, this number will be the
  National Telecommunications and Information Administration (NTIA)
  serial number assigned by the FTIA.


So if you are trying to obtain frequencies for a military base, which may be working with local FAA facilities, you will also need to get the NTIA/FTIA data.

The FTA is public information, but I am unaware of an Order or publically accessible database for the FTA.  When I see an avionics inspector later today, I will ask her if she knows where FTAs can be looked up.