There are some posts spread on the forum which can help you to get started and/or understand some settings which may be useful for you. In the base, Syncthing can and does use local connections where/when possible. So if you disable the WAN-related settings it should get you already to a solid point for your use-case. Also please note that Android + discovery is a difficult subject though, there are quite some topics on the forum about that which are probably worth looking into as well.
Limit Syncthing to only use local network: Review and suggestions appreciated (a bit of a summary of options that have to do with global/local connections, you may want to read through the entire thread to see what’s of use and what isn’t)
How do I stop it from blabbing to the world? - #4 by Nummer378 (it’s advised to not scroll through the entire thread here as it was otherwise a bit toxic, but this comment had good input).
I think for your case disabling relay and global discovery will prob do quite a lot already. Then also set allowedNetworks allowedNetworks — Syncthing documentation to just your LAN’s network address. From that point on it’s more or less checking what settings can help in making it more silent to the outside world.
And as a side-note; it’s now also an issue on the docs-repo; Tuning article for avoiding any Internet/non-local chatter · Issue #834 · syncthing/docs · GitHub