I want to test new functionality, that included in Android 15 Beta
This functionality marked in documentation like that:
Added in API level 35
Also in S Extensions 13
I want to install this Extension 13 (as it allows to use added functionality on older Android versions), but I can't see it in SDK Manager (in Canary Android LadyBug either), just Android SDK Platform 35 and Android SDK Platform 34-ext12
Why is that? Is it expected to appear after Android 15 release?
Yes, that is correct, from past Android releases the extension version only comes out after the stable release. Hopefully by next month.