Chiming in here:
I still use LINKSYS WRT-54G wireless routers running DD-WRT. They all support TELNET logins (port 23), which is the insecure predecessor to SSH (port 22). I use TELNET to log into them when I wish to do something 'internal' that is not directly supported by the web interface.
LANTRONIX used to make a print server that had 10BASE-T ethernet to CENTRONIX parallel port AND RS-232 (EPS-1 and? EPS-2). It supported many TCP protocols ... including TELNET. I have one of each in storage and used them both back in early 2000's. See PDF attached. It would be the ideal solution for an "INTERNET BBS" run transparently to the Z80 BBS.
So all you really need is a protocol converter, TELNET to RS-232 (or TTL serial), which makes the TELNET connection transparent to the Z80-run BBS using RS-232. If you are to host this Z80 BBS using a TELNET-2-RS232 converter in your home (or business) and you don't have a static IP address assigned to your INTERNET connection, then you would need to acquire a dynamic DNS account (i.e. ) to auto-magically map your chosen domain name to your dynamic IP address. You would also need to assign a static IP address to the TELNET-2-RS232 converter's MAC address, so it has the same IP address assigned on your internal IntraNET, then create a port-forwarding formula on your router to map an incoming INTERNET IP/PORT (i.e. port 8023) to the TELNET-2-RS232 converter's TELNET port, which is 23.
I should also mention that a linux box (Raspberry PI) running SOCAT could *easily* be used instead for TELNET <-> TTL-serial.
As is usual in these days of "modern computing technology", you just need to emulate what you require. Be it in software or hardware.
Hope this info helps...
Peace and blessings.
Scott