If/when you purchase CCleaner for Android through the Google store (or 'Upgrade' from within the app itself) it activates automatically through your Google account.
You don't have to download anything extra, you do not get a seperate licence key to input, it's all done by Google Store.
CCleaner Pro will be activated on all devices that log into the Google account it was purchased from.
If the Pro features are not available in the app then check that you are signed into the correct Google account.
This tells you how to check that you have a valid CCleaner subscription on your Google account: https://support.ccleaner.com/s/article/how-can-i-activate-a-previously-purchased-ccleaner-android-pro-subscription-on-an-alternative-device?language=en_US
Note that you have purchased your CCleaner for Android subscription from Google Store - CCleaner Support will have no information about that purchase, they won't even have a record of it.
If you have problems with the payment or activation it is the Google Store that you need to contact.
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If you have purchased a multi-device/multi-OS licence for CCleaner from CCleaner. (eg. CCleaner Pro Plus or Premium) then you do need to activate CCleaner for Android with your existing licence key - unless you want to also pay Google for it.
The instructions for how to use an existing Pro Plus/Premium key to 'Activate' CCleaner for Android can be found here: