Running Android 13 on a device from 2011 is a testament to the optimization skills of the developer community. However, you must temper your expectations.
Currently, the Galaxy S2 (specifically the i9100 model) has strong support thanks to dedicated developers. The version you are looking for is likely (which is based on Android 13). samsung galaxy s2 android 13 free
Installing standard Google Play Services will completely freeze the device. If you want apps, you must use ultra-lightweight alternatives like MicroG or open-source stores like F-Droid. Running Android 13 on a device from 2011
Modern Android versions have improved security patches compared to Android 4.1 Jelly Bean, which was the last official update for the S2. you must temper your expectations. Currently
Boot into TWRP by holding Volume Up + Home + Power.