You should have no problem jumping right into 3, I did the same after playing Elden Ring. It's a complete story on its own. The only thing that might be confusing is when there is just a room that deadends without any loot or enemies, and it's usually because in DS1 someone important was in that room and it is there as a reference for the DS1 players and to show how much things have changed in the time between the games. If you really want to you can always watch the intro cutscene for DS1 and look up some lore on the main characters/bosses either on the wiki or in YouTube videos. I've never played DS2, but from what I have seen it is mostly disconnected from 1 and 3 lore wise