It seems the implementation for said toy HTTP server is quite dated and bug prone. I envision to use Boost Beast to replace the minimal HTTP responder that is currently used on top of the ASIO stream. To be clear: this does not aim to implement a fully functional HTTP server. Instead, it should serve as a nice showcase for how to combine ASIO, Botan's TLS and Beast to build an HTTPS server.
Perhaps, @hrantzsch's example code could be a good starting point for this. This example was initially adapted from Boost Beast's server example in early 2020 and may or may not need some refreshing with the latest Boost code.