On a fresh install of Android mode 4.5.1, when selecting automatic Android SDK installation it completes the ~250MB download but then fails with a "Bad news" error message.

For anyone else running into the same problem, I managed to set the SDK up manually in the following way:

1. manually download the Android SDK Command-Line Tools and extract them into youruserdirectory/Library/Android/sdk/cmdline-tools/latest
2. run ~/Library/Android/sdk/cmdline-tools/latest/bin/sdkmanager "platforms;android-33"
3. back in Processing, open Android mode, choose manual SDK and select the youruserdirectory/Library/Android/sdk directory