In the ☰ menu, Share creates a link that contains the whole patch: modules, cables and settings are compressed into the address itself. Send it to anyone: when they open it, they get your patch, ready to play.
Nothing is stored elsewhere
The patch travels in the link, not on a server: ModularSynth has no server for patches. That is also why a very large patch can make a very long link.
Opening a link
If you already have a patch open, ModularSynth asks before replacing it. Save it to My Library first if you want to keep it.
In this documentation
The Try it in the synth buttons on the module pages and the Open buttons on the presets use these same links.