The Warped Potion mod might be a misleading name, as the potion itself isn't the main feature, but rather the effect. It allows for you to teleport back to where you drank the potion or got the effect, being good for adventuring and confusing your enemies.
The Warping effect will save your position when it is first applied, and teleport you back when it is removed. The three ways that it can be removed are by commands (/effect clear), drinking a bucket of milk, waiting for the time to expire, or getting a new instance of the effect by drinking a new potion or otherwise (It will wait until you are teleported back before applying the effect again). If it's removed while they are in a different dimension than they started in, it will not teleport the player.
The Warped Pearl can be made with 1 ender pearl and 1 warped fungus. When thrown, it gives a 7.5-second warping effect. Note that the effect is given when it is thrown, not when the pearl lands. So if the pearl takes more than 7.5-seconds to land, you will not teleport back. I can see these being useful for PVP when you want a quick sneak attack without giving them much time to get any hits in, or maybe in quickly teleporting into a bastion to get some treasure, getting away before the brutes notice you. The Warped Pearl, just like Ender Pearls, can only be in stacks of 16.
The Warped Fruit is made with 1 chorus fruit, 1 sugar, and 1 warped fungus. When eaten, it will give 15 seconds of the warping effect, acting as an alternative to the Potion of Warping when you don't need much time and don't need the hassle of brewing. These can be useful for when you are going into a potentially dangerous place that you don't want to stay in for long. Because of the fact these are a food item, you can feed them to mobs like foxes, and the effect works on them as well! It's very funny to watch a fox about to kill a chicken by pouncing, just to be teleported away.
The Potion of Warping is made by brewing an awkward potion with one of the 2 warped items added by this mod. The base potion gives a 1-minute potion of warping, which would be good for splash potions, lingering potions, or tipped arrows if you want to confuse an enemy or get somebody off your trail. Adding redstone dust will boost it to a 15-minute potion, which could be good for if you need to go to a friend's base to drop something off without worrying about traveling back. Adding a block of redstone to the 1-minute potion will make it 1-hour long, perfect for a short adventure, and adding a redstone lamp to that will make it 3 hours, perfect for long adventures. If you are ever about to die while you have the effect, you can drink milk to go back to where you drank it.
Do note that by the nature of potions, any effect longer than around 25 minutes will show up as : in the inventory, so for the 2 longer potions, you won't know how much time is left until you have 25 or so minutes left. It's also extremely important to be in the same dimension you started in when time is almost up, as if you don't, the warp will fail, leaving you stranded.