but the idea would be some service/website/app where I could put all my wallets at once to track them, the balance and notify me of any transaction/movement
BlueWallet as suggested by Zaguru12 should do that just fine, It's been some time since I last did it but you should be able to import the master public key of your wallet, and it will notify you whenever there is an incoming transaction in any of your wallet's addresses. You should also be able to import multiple wallets, and not just one.
The apps I suggested should also do that and more
(not all features are free though).