You read that swashbuckler deed correctly

The swashbuckler deed precise strike, an extraordinary ability, does, indeed, allow, for example, a level 20 swashbuckler that possesses at least 1 point of panache and that attacks with a light or one-handed manufactured piercing melee weapon in one hand—and doesn't wield in his other hand a weapon and doesn't in that other hand carry a shield—to deal with that weapon an extra +20 points of precision damage.

The deed forces a lot of conditions onto the swashbuckler, essentially mandating he employ a very specific—and widely considered suboptimal—fighting style if he wants the benefit of the deed precise strike. The swashbuckler earns that +20 points of damage (that only affects those foes vulnerable to precision damage and that isn't multiplied on a critical hit).

You deal damage

PHB page 194:

Resolve the attack. You make the attack roll. On a hit, you roll damage, unless the particular attack has rules that specify otherwise. Some attacks cause special effects in addition to or instead of damage.

Stunning strike does not say you do not do damage. PHB page 79:

Starting at 5th level, you can interfere with the flow of ki in an opponent's body. When you hit another creature with a melee weapon Attack, you can spend 1 ki point to attempt a stunning strike. The target must succeed on a Constitution saving throw or be Stunned until the end of your next turn.