You can have a complete tcp/ip stack and an embedded web server in a 8bit micro using only a handful kilobytes of ram. This is (used?) to be a good way to service super-simple configuration to the user without having to connect through a serial cable and without too many additional parts.

There's absolutely no chance that 8bit can do TLS though, and with browsers refusing to connect without https what is often done in the embedded space is to have a separate mcu which is just doing wifi+tcp+webserver. That mcu is 32bit or better (any of the espressif families for example), often eclipsing the power of the rest of the entire system.