You can only do this for a player’s friends using Player:GetFriendsOnline(), it returns a dictionary of players with their location type. Player | Documentation - Roblox Creator Hub
What about somehow get random friend of that player and then use Player:GetFriendsOnline() like @bytesleuth suggested, but use that friend to get your status?
Got it to work using the /v1/presence/users endpoint instead, no authentication required:
--Enable HttpService through game settings
--If the place isn't published run game.HttpService.HttpEnabled = true in command bar
local HttpService = game:GetService("HttpService")
type presence = {lastLocation: string, lastOnline: string, userId: number, userPresenceType: number, name: string?}
local url = "https://presence.roproxy.com/v1/presence/users"
local body = HttpService:JSONEncode({userIds = {544088422}})
local names = {"Offline", "Online", "In Game", "In Studio"}
local response = HttpService:PostAsync(url, body)
local presence: presence = HttpService:JSONDecode(response).userPresences[1]
presence.name = names[presence.userPresenceType+1]
print(presence, presence.name)
This endpoint accepts and can return multiple user statuses at once, so instead of making multiple calls at once, you can just send multiple userIds at once(the maximum userIds at once is 50).