Given your experience in electron I think the shortest hop is going to be React Native. Especially since half of the requirements are server-side.
Google is doing a pretty great job bringing up Flutter and the tooling is pretty great. For me however, dart seemed like quicksand and not everything is in its final home.
React Native is mature, and considering my cursory analysis of your experience and the low complexity of this project, you've got quite a lot of room to grow into Javascript Land.
Ultimately, my recommendation is always "play with both, see what you like, and get to know the documentation and the community." Keep your head on a swivel and set aside time to peek greener pastures, but spend most of your time delving deeply into what you're already doing.
But yeah, go with React Native first, get bored of it, learn what the shortcomings are through experience and then see if something else is really more attractive or just a new shiny.
