That may what sysadmin meant back in the 80s and 90s but it's not what it means now. I would never describe myself, a SRE-SE, as a sysadmin because I would be describing someone whose primary job is to operate software and iterate on configuration.

SRE-SEs on the other hand are SWEs, they just have a focus in systems adjacent software whereas a SRE-SWE is someone who can dig into compiler level issues and optimization. Both write application code, do analysis, and write policy. A sysadmin of today would be out of place on a team like that.