I bought the game on one device, but the full version of the game did not open on a different device that was connected to the same account.

Please make sure that the Google Play account used during the purchase of the game is the same account as the one connected to the device. If there are multiple accounts connected to the device, it is easy to accidentally use the wrong account. To switch the active account, click on the account address located at the top of the Play Market app settings panel. If the active account is the same as the one used for the purchase, then delete the game from the device, restart the device, and reinstall the game. The purchase should be restored automatically upon starting.