Google recently released Android platform 36.1 tied to the upcoming Android 16 QPR2 release, installed in the expected $ANDROID_SDK_ROOT/platforms/android-36.1 location.
Unfortunately, cargo-apk doesn't seem to recognize non-integer android-XX values, so builds end up failing with "Error: Android SDK has no platforms installed." instead.
I don't know how commonplace this is going to become in the future, but I suspect it will be as they've also changed their Gradle DSL to accommodate minor API levels now as well.
https://developer.android.com/reference/tools/gradle-api/8.13/com/android/build/api/dsl/CompileSdkSpec