Bought it on Google Play Store but didn't receive an activation code: did something go wrong?

No, in most cases nothing went wrong. If you buy a Protectstar app through the Google Play Store, you do not receive a separate activation code or license key. Activation happens automatically through the Google account used for the purchase. Protectstar explicitly states that Play Store purchases are managed through your Google account, which is why no additional code is issued.

How activation works with Google Play:
After the purchase, the app should automatically recognize the paid edition or feature. The important point is that your device must be signed in with the exact same Google account used to make the purchase. Google itself explains that you can switch between multiple accounts in Google Play. If the wrong account is active on the device, a purchase can appear to have “disappeared” even though it is simply tied to a different account.

What you should check first:

• Open the Google Play Store and make sure you are signed in with the correct Google account.
• Update the app to the latest version.
• Restart your device once.
• Open the app again and check whether PRO, Premium, or Lifetime is now displayed correctly.
  Protectstar also recommends restarting first if there are problems with in-app purchases. In some cases, the purchase can then be triggered again without being charged a second time, as long as the same Google account is being used. 

How MY.PROTECTSTAR fits in:
A MY.PROTECTSTAR account does not create a retroactive activation code for a Google Play purchase. So it is not an error if you register there and still do not receive a code. Shop purchases work differently: in that case, you receive an activation code that you can assign to your account. For Google Play purchases, however, the actual purchase and license logic remains tied to Google.

If it still doesn't unlock:
Then it is best to send support a screenshot of the app, your proof of purchase, and—if available—the GPA number from the Google receipt. That makes it much easier to determine whether the issue is related to the account, an activation that has not yet been recognized, or a technical edge case.