this isn't the shiny chance, this is the boost you get once you have a stored shiny and it's based on the best weight you had for this fish (not only shiny). But i agree that it's a bit unclear in the game because the thing that is boosted is shown below the number (Fishing xp in your 1st screenshot), i feel like it would make more sence to put it next to the number.
And remember that the base shiny chance is around 0.01-0.02% (you can check yours in your profile by pressing 'p'). So its normal if it takes a long time.