I´m doing the new quests here atm. Once you start questing, you get a buff everytime you are under water that increases your swimspeed and you can breathe. Most of the quest items are on the ground and you can "walk" on the ground. But its slightly faster than swimming. Its not much, maybe 20-30% faster this way to reach your destination.
- swim down on the ground
- walk to your locations
- save time
Have fun.