It's unsafe even if the code is perfect. The webapp loads from the website. They could serve you a different one if/when you become interesting. That special app doesn't need to have bugs, just be different in inconvenient ways.
Discussion
Not if it comes signed and an extension checks.
Still you must trust the author.
But that is true for all software. We must transition to software-less computing. Semi-analog AI processors might be a long-term solution.
People will train their AI and share their trusted models generation after generation. Code-free computing.