Destiny 2 has an anti-AFK system where if a player isn’t interacting with the game enough they will be removed from the lobby. Single button/key presses and wiggling your mouse/thumb sticks are not enough, you must be moving about. You will have to interact with the game like every other activity in Destiny.
Also, it is highly recommended you pick up your fish immediately (takes 5 seconds or less) to avoid triggering a GUITAR error (occurs when there are too many objects on the ground) which will lead to disconnection and loss of fish.
The likely reason we have to constantly move around is to stop people from using macros and other malicious tools to stay in the lobby. It is very unlikely Bungie will change the AFK system as any change will lead to instant abuse.