I think most people recommend using an extension that doesn’t share your private key with the client. The one I use is the nos2x chrome extension.
Discussion
Is Ably considered as one of such extension?
And if Alby or any other browser extensions would still be vulnerable to the security holes in any particular browsers?
I’m not familiar with Ably and don’t have the technical expertise to answer your question about different browsers. It’s an important question though. I’d love to know what you find out. (I’ve been using Brave and the chrome extension.)
I hope to find answers to these questions as well. I'm not a programmer and these stuff are outside my skills level.