To clarify, it sounds like fishing will only be available as a free upgrade if you own the Special Edition, so your base game from 2011 probably won't work. Skyrim: Anniversary Edition and the next-gen update will launch simultaneously on November 11.
But don't worry, you won't need to buy the Anniversary Edition to get fishing, as it's one of three features included in the also just-announced Skyrim next-gen upgrade, which will be free if you own Skyrim Special Edition on PC, PS4, or Xbox One. The exciting - no, relaxing - new feature was announced alongside Skyrim: Anniversary Edition, which bundles together more than 500 community mods and launches this November.