It was originally planned to support TLS(the transport layer for HTTPS) in MMBASIC, but the author eventually abandoned this as unworkable(having seen how the network support was kludged in I’m not surprised). The author has since stated his preference to use a coprocessor with onboard TLS support for future MMBASIC network-capable devices, so possibly the manual reference originated from something which was never released or will exist in the future.
Basic compiler MachiKania type P for PicoCalc does support HTTPS, which for me is a quite a distinctive point in favour of it, since most of the interpreted languages available for PicoCalc either have no network support or no TLS, which in practice, since most websites will force HTTPS these days, mostly limits you to connecting to your own specifially set up local server.