Reinstalling your Mac does not require buying Diarium again. If you paid for the macOS version before, sign in to the Mac App Store with the same Apple ID and restore the purchase. A Google account used for sync on your Mac is not the account that owns a Mac App Store purchase. Your Android purchase remains valid on Android.
The separate-purchase rule is stated on the website, in the store description, on the Pro purchase page (including the button), and in the Pro version FAQs. Have you read those FAQs? If you did and something was unclear, please tell me which wording led you to expect that the Google Play purchase would cover macOS. I want to improve it where I can.
You say you also paid on your Mac. Please check your Apple purchase history for that macOS payment. If it’s there but “Restore purchases” still fails with the same Apple ID, email me the purchase details privately so I can help investigate.