DON'T PANIC, but do heed this word of caution. There is nothing new here, but the risk they are talking about is genuine and not limited to Coinbase.
In the crypto world, there is a mantra, "Not your keys, not your coins." Simply put, if you leave your Crypto on an exchange, ANY EXCHANGE, you don't own it. The Exchange does.
It is essential to understand that the actual Crypto always resides on the blockchain. The only question is who controls its keys and how securely they guard them. Owning Crypto is deceptive, as what you own is the control of an address on the blockchain via private keys. Anyone who has those keys, or the seed phrase that created them, can access the Crypto. We can consider the keys and the seed phrase as equivalent for this discussion.
Exchanges hold the keys. YOU DON'T HAVE THEM! Hence the mantra. Wallets let you control the keys. If the Exchange goes away, you are in trouble. If you lose a wallet, you can reconstitute it using the keys or the seed phrase. BUT DON'T LOSE THE KEYS!!!
There are FOUR ways to hold Crypto. (1) On an exchange, (2) In a HOT Wallet, (3) In a Warm Wallet, and (4) In a Cold Wallet.
An exchange, such as Coinbase, is a place to buy, sell, and hold Crypto such as bitcoin. Think of it as being similar to buying and selling stocks on a broker such as Schwab. When you buy Apple Stock on Schwab, they hold it in your account. You don't get the stock certificate, much as you don't hold the Crypto keys. The Exchange does. You don't have the keys, the only link that says you own it is the exchange accounting. This is great for rapid buying and selling and other forms of investing such as staking and borrowing against it, like a margin loan. However, you are at the mercy of the Exchange. As this article points out, getting your coins may be challenging if the Exchange disappears.
A HOT wallet is an online wallet controlled by the Exchange. Metamask, Coinbase wallet, and Edge wallet are examples of HOT wallets. They are always on the Internet, potentially subject to malicious attacks leading to key theft, but safer than the Exchange. A hot wallet stores the keys online and controls access via Public Key Cryptography.
A WARM Wallet is similar to a hot wallet but is downloadable to your device. It is mainly offline but can access the Internet for purchases, trades, and other uses. Atomic Wallet is an excellent example of a Warm Wallet, and it is a good one. However, in theory, it can also be subject to attack as it resides on a connected device, plus you might lose the device.
A COLD wallet is a separate device, usually taking the form of a USB flash drive. This is the ultimate protection. It never goes online, and synchronization with the blockchain happens through an interface app. If you lose it or have it stolen, the contents are encrypted so the thief can't get into it, and you can buy a new one and recover your Crypto with the keys.