I'm using the Coinbase Wallet, it's self custody, a continuation of the Bread Wallet (BRD). I think they were acquired 5 years ago.
It works well and has the advantage of tying as much as it can into the Coinbase ecosystem. It's still self-custody and I find it usable.
Hello, does it have anything to do with Coinbase (the company)?
You mention that it's self-custodial. Does it require a coinbase account?
Finally, what makes it unique?
A simple search and test would give you an answer. Plus we in the Bitcoin community follow a Golden Rule -
Don't Trust, Verify.
But because I was also curious, I tried the wallet and I have verified for MYSELF that the wallet doesn't actually need a Coinbase account. It's a wallet with your own keys that could receive Bitcoin, and all sorts of shitcoins. Because it's a browser extension, I advice using a Ledger hardware wallet. It's the only hardware wallet allowed to connect with Coinbase wallet.