So clearly there's something mysterious about this stone. Clicking on it in the map would give off this stone sound and close the map. Your fishing line goes through it, you can pretty much "fish inside" the rock. (Nope, just the common fish) However, it is marked on the map like it has some sort of importance. What are all the things you've tried, could this be something in development or is it already possible to solve the mystery surrounding this rock? Maybe it is something that will get revealed with the upcoming update?
As far as the game files are concerned, the rock doesn't do anything at this time. No characters/villagers talk about it, no lore hidden in the game files, and it has not been mentioned by ConcernedApe yet. In the future, it could be used for something, but for right now, it's only there to make a noise on the map. Source: https://stardewvalleywiki.com/Secrets#Lonely_Stone
The update (same one as multiplayer) is supposed to have some boat-related content, so maybe it'll tie into that. Who knows?