I dont think using syringe in long run helps. Pardon me if this is incorrect. But if you are using formula milk, introduce bottle fed. And this definitely do not interefere direct latching. Why do I say so? Because in this modern era, we have many types of brand bottle that has bottle teats similar to mummy nipples. Well not 100% but it replicates it.
And in the long run, if your baby grow up and you have to wean off, you will still have to introduce milk bottle. Baby's get irritated/agitated because they dislike it. So make a change.
Both of my kids direct latch and use bottle for FM/BM.
The only reason most babies sometimes on the other hand prefers direct latch because of mummies smell, bonding between you and them.
So try to introduce milk teat instead of syringe.