If you are looking for real-time file availability for 1000s of machines, you are looking at the wrong solution and you are probably better off having a shared file system (be it NFS or S3+fuse if you can afford the latency for the scalability).
https://data.syncthing.net/ says there is someone with 2.2k devices, yet I have no idea what their topology looks like, and we target “I run syncthing at home between my N computes” use case (where N is in signle digits), so it’s not something we test for.