Good question. I had to think about it and I can't get more definitive beyond "it depends".
In many ways, it's already the case. Browsers are already possible through partnerships with companies that manage certificates, DNS and so on. They also have special APIs that are open only to the vendor. You can't spin off your authoritative DNS or certificate authority or malicious site detection and have it made accepted by Firefox/Chrome or others.
On the other hand, we have an understanding about what web is and expectations about the web standards which makes me to expect neutrality. It's the tool that promises me to parse whatever HTML I throw at it and execute any JS.
Then we have things like Brave browser that has API that's not of any standards.
So, I don't know. It depend. I will know it when I see it.
That's a bit of a funny example, since it looks to me like that's Chrome giving special treatment to it's own store? And offering APIs for the store to function, like showing installed extensions differently from non-installed ones?