You gain Stealth by fishing in secret areas with equipment modified by Earl. It works just like Pole Leveling, but has requirement of fishing in secret areas when your pole is modified by Earl. Fish in secret areas require certain Stealth Levels. It currently maxes out at 25. Each pole requires different amounts of XP per Stealth Level.
Pole Leveling special bonuses also boost Stealth Leveling.
Stealth is a special attribute added in with the Secret Level release in 2021, to unlock Secret Levels - simply visit Earl's House