Is there a browser extension that works similarly to Ethereum's Metamask? I am wondering that if there isn't one, is it because of some technical limitation, or that just no one has gotten around to developing one.
There is a Bitcoin wallet extension for Chrome. It's apparently used by 1500 people and has 3.5 stars average review. Still, I would not trust this extension without first auditing its source code. I cannot find its code on its author's Github profile.
CoinSpace is a web-based Bitcoin wallet. It's not exactly an extension but if you understand what Metamask does you'll see that it isn't really different.