2D Pathfinding with platformer

I’m working on developing a game that would require the player to move to a specific point on the screen based on a mouse click/touch. The game will essentially be a turn-based, platformer that is laid out on a grid. Paths won’t be too long, only a few grid squares at time, so not super intensive pathfinding. I’ve been looking for information on how I can make that mechanic work, but I’m not knowledgeable enough to know what would work best for my game and with Unity. I did find this Platformer Pathfinding asset in the store, but it’s a bit old and I’m not sure it will work. Does anyone have any suggestions on how I could implement this kind of mechanic (with the mentioned asset or otherwise)?

I will assume there are some obstacles to avoid. For such small distances, A* search is sufficiently strong and easy to implement pathfinding algorithm.