I just remembered player GUIDs. The second part is a realm ID and connected realms share that ID.
https://wow.gamepedia.com/GUID
Lua Code:
local guid = UnitGUID("player")
local kind, server, ID = strsplit("-", guid or "")
-- example: guid="Player-970-0002FD64" kind=="Player" server=="970" ID="0002FD64"
For example, if you were on (NA) Blackrock, the middle number will be 10, but if you were on (NA) Earthen Ring, (NA) Auchindoun, or (NA) Cho'gall, which are connected together, it will be 101. The server in the example, 970, is the connected realms "Beta Leveling Realm 01" and "Beta Leveling Realm 03".
CensusPlus "figures this out" with a fork of
LibRealmInfo named "LibRealmID". The original lists each server as their original ID with a connection data table while the fork combines the data into one table with "ID-servername" keys.
You'll have to arrange Skillet in a way that remembers the GUID of each alt and allows sharing between characters that have the same server ID in their GUID, which means users have to login to each alt once your change is released to save each GUID.