Demos are in Documents\My Games\FTL-Rewind\profiles\<profile>\demos. Only finished .ftlrwd demos up to 10 MiB are taken; damaged or edited files are refused.
Documents\My Games\FTL-Rewind\profiles\<profile>\demos
.ftlrwd
Without signing in, the demo is listed unranked and not linked to any account. Sign in through Steam to rank it.
By uploading, you publish the demo: anyone can download it. The demo holds what the game wrote into it, including the name and comment you typed at the run's end.