I'm using IDE version: 2.0.0-rc5, date: 2022-03-10T11:09:10.332Z, CLI Version: 0.21.0 [10107d24] to program an Adafruit PyGamer. It looks like the library folder for the ARM Toolchain is: C:\Users\EagleAglow\AppData\Local\Arduino15\staging\packages
In that folder there are two Toolchain library zip files: "gcc-arm-none-eabi-7-2017-q4-major-win32-arduino1.zip" and "gcc-arm-none-eabi-9-2019-q4-major-win32.zip"
The most important thing to understand is that the IDE doesn't have any toolchains. It is only a general purpose tool for developing Arduino sketches. The Arduino build system is a very flexible framework that allows the creators of boards platforms to install any arbitrary versions of any arbitrary toolchains needed for their target hardware, and use those toolchains in any way they want.
This is the folder where the Arduino IDE stages the downloaded toolchain archives before installing them. Once the installation process is finished, the files under that folder are never again used by the Arduino IDE. They are never cleared out by the Arduino IDE, so the presence of a given version there only indicates that it was installed at one time, and not necessarily that it is currently in use.
The toolchains currently in use are under the C:\Users\EagleAglow\AppData\Local\Arduino15\packages folder.
Why do you want to use it?
Unless you have some specific reason for needing the new compiler version, you might be better off to leave the boards platform maintenance to Adafruit and get straight to having fun with your PyGamer.
If you are set on it, just study the information at the Arduino Platform Specification link I shared above and you will get it sorted out eventually.
No. As I explained this is completely independent of the Arduino IDE installation. It would be many gigabytes if Arduino bundled every possible toolchain. Much better to install the toolchains as needed for the specific boards each user happens to have.