Are there any plans to rewrite the browser implementation in the Jakt language once that gets a bit more stable? Memory safety would be a unique advantage over other browsers (aside from Servo).
I am also looking forward to that, but I think the Serenity philosophy is to not make any long term plans and commitments.
If the language becomes mature enough, and there are people interested enough in doing that porting, it will likely happen.
I think their C++ code is also constrained enough due to the use of their custom standard library that it would be possible to write a transpiler from C++ to Jakt.
There are no concrete plans for anything with the Serenity ecosystem. But the main design goal of Jakt was originally for developing mainly GUI applications in SerenityOS. But if Jakt ever gets used in SerenityOS, a gradual rewrite of the libraries underlying the browser engine seems likely to me.
I will note though that development on the Jakt language has slowed down significantly. After extremely fast initial development, most Serenity developers no longer contribute to the language. Because everything is done exclusively when the contributors feel like it, development happens in bursts. And right now, Andreas is not actively working on Jakt, so very little improvement is happening there. The main developer working on the language is Ali Mohammadpur, but I don't think he is currently being paid to work on the project. So his contributions are also inconsistent.
If the language becomes mature enough, and there are people interested enough in doing that porting, it will likely happen.
I think their C++ code is also constrained enough due to the use of their custom standard library that it would be possible to write a transpiler from C++ to Jakt.