Does Unstoppable have a "scan all blockchains" feature or something like that, where the software will go through all supported assets to see if there are any transaction records that correspond to your portfolio? I highly doubt it, but it doesn't hurt to ask. Or can you access the complete transaction history associated with your wallets without adding individual coins to the software?
You better remember or take note of what you transfer there. That's the safest way. Going back to Ledger Live, when you install the software, its portfolio view is completely empty and doesn't show any balance either. You have to add the coins and tokens to it and let it scan the blockchain before it can display your balance. It's the same thing. If you forgot you moved a certain altcoin to your Ledger and don't have the app installed on the device or the coin added to your portfolio, you wouldn't know it's there. What I don't know, though, is if your wallet's transaction history will show records of transactions you performed that currently aren't part of your portfolio view.
So this problem is not only with Unstoppable Wallet but with Ledger too. I am sure then there will be no way to scan all the blockchain in the trust wallet too.
This leaves us with only one option and that is to write the altcoins on a piece of paper or digitally somewhere, so if the coins are removed from the portfolio view, you know you have which coins in your portfolio.
By the way, I do not know why these wallets do not have such features and no one ever talked about it as we should have this feature