FWIW, it's possible that the lat/lon on the Seestar's watermark is purposely not accurate so you're not literally broadcasting your exact home position every time you post a pic.. It doesn't actually need to be all that close to get an initial fix because it uses plate solving to get actual position and scope attitude (horizontal calibration).
That said.. virtually all modern cell phones (and some tablet) have a built in GPS receiver but they generally determine their location in 3 ways..
It takes quite a lot of heavy calculations to determine your initial location with GPS and maintain it at all times, so they simply don't do it unless needed by an app that demands high location accuracy.
Phase 1 gets your general location with combination of cell tower proximity and nearby wifi network identification.
When you first start Google Maps you'll see this as a large blue circle (can be a couple hundred meters radius) around the location it thinks you're at.
In Phase 2, the cell phone picks up direct GPS satellite signals (if outside, or not too deep into a house), but it doesn't do the heavy calculations itself. It just sends the raw GPS data to the cell network, and it does the math and sends back your exact position to the phone. The cell network knows your general position because of the tower you're on and thus always knows which GPS sats are overhead your position, which eliminates the need to figure out the initial fix. This gives you good position accuracy relatively quickly..
When this happens you'll see that large blue circle in Google Maps shrink to a small one only 2-3 meters across.
Phase 3 occurs either after 1 and 2 are complete.. or not possible due to no cell coverage or.. you fire up some sort of GPS specific application (like GPS Status for android). Then it will both receive the GPS signals and do the processing onboard.
The problem is, if start this phase while out of coverage, then it can take a minute or two to get the initial fix, longer if much of the sky is obstructed.
If you put the phone to sleep it may lose this fix, but it should regain it relatively quickly after it wakes back up If I need it to keep its position continuously I'll fire up my GPS Status app, and it'll keep GPS receiver awake even when the phone is asleep. You wouldn't need this for your whole Seestar session, but you could fire up an app like this a few minutes before you start up Seestar scope, and then shut it down after the scope has your initial fix.
To see Phase 3 in action, just put your phone in airplane mode and then fire up Google Maps. You may see no blue circle at all initially, then it'll eventually appear large, and quickly zoom on your position. If you want to see how long it takes to get a cold fix, put it airplane mode, and restart the phone (it'll stay in airplane mode), then fire up maps or gps status. You'll see it can take a minute or 3 before it has any clue at all where you are, but once it has a few sats it'll go straight to your position, with no intermediate large circle.