What Supported OS can I put on 2009 Mac Pro ?

Apple had many opportunities to block installing MacPro 5,1 MacOS on Mac Pro 2009 hardware with the Mac Pro 5,1 firmware installed. To date, they have not chosen to do.

Going beyond Mojave requires additional hacks. Some features begin to fall away, such as the stock Wi-Fi card, but there are newer Wi-Fi cards that can be installed with additional hacks.

MacOS 10.13 Ventura code introduces machine instructions that are not possible except with semi-emulation, so you really only have one more year before it will go unsupported. But if the machine is not on the Internet directly, its risks are reduced.

Stock standard Mac Pro 4,1 is supported to run up to 10.11 El Capitan.

Users who have hacked** it to install the MacPro 5,1 firmware have turned theirs into a Mac Pro 5,1 for all intents and purposes. Mac Pro 5,1 is supported to run up to MacOS 10.13 High Sierra unmodified, or 10.14 Mojave if a metal-capable graphics are is installed. Some users have used additional hacks to press on a few more versions.

** this is not without some risk, you could turn you Mac Pro 4,1 into a non-functional BRICK.