Does Python still have performance issues? That's always been my concern when considering its adoption.

Yes it does, and almost everything else will have performance issues except assembly. With web services, chances are that you'll hit other bottlenecks before you hit it. In python you have multiple ways to optimize performance, for example use PyPy, or various libraries like Cython that compile your performance sensitive code.

That's how asyncpg can outperform[1] some libraries that you normally would think was not possible.

[1] https://github.com/MagicStack/asyncpg