Ah! People think of VPNs a bit narrowly now because of all of the commercial VPN companies, but VPNs can really be what they say on the tin "virtual private networks". Basically you set aside a private IP range for your network and you can tunnel traffic between devices as though they're all on one big LAN. This is often used to access internal resources remotely, and the VPN is used to authenticate your access to various servers. So, for example I can access my home servers to clone git repos or whatever from a wireguard VPN, but those servers are otherwise not exposed on the broader internet.

I think I'm confused about your use case, though. You're using somebody else's sync servers, but you can have an IP blocklist on them? What do you mean your app connects to the sync server? What devices is the app running on? Is it just your personal devices, or is it an app that other people would use? I think some more details might help people get you to the right solution. Would be good to know why you want an IP blocklist, what this is for specifically, where the blackllist is, and what you actually have access to changing!