(my opinion)
Anything with "designer" in it, isn't a coder. HTML / CSS could be considered fringe "coding" and with React, html is used in JS as JSX, so I'd consider that person a developer. Designers generally just design, with their primary tools being Photoshop, Illustrator, etc... where a developers primary tools are a text editor and an FTP client.
Even with NodeJS acting as a server in some situations, I still won't call a front end developer a full stack developer. As a full stack developer, your responsible for the full stack. Thus, this can include configuring your server environment, as well as everything else including but not limited to CDN, Load Balancer, DNS, file storage, any RDBMS, etc...
As you said, this can go on and on; there are people who only do systems administration and no programming - these are not developers obviously. There are people that only do development and no systems administration. These are not systems administrators or full stack developers.
I've never considered myself to have any specific title other then full stack developer - it's just about 10am here and since 5:30am I checked to make sure all the servers were healthy (systems admin), made sure all the emails that were supposed to go out, went out (sys admin), installed a new pc for an employee (help desk), configured a new pc (sys admin / help desk), ran a new network line (general contractor? hah) and now on to some development.