Thanks for the more thorough analysis!
So yeah as the checkpoints are in the game, they only save the location of the player and not the item the player is carrying, so I ended up putting a checkpoint near the pickup point, so the player doesn't have to walk back to the pickup point if the item burns. This was a decision I ended up making while trying to keep the core gameplay more simple. Was it the right choice? Not sure really.
About the coyote-time, there kinda is one, I made it using a ray collider that is located near the feet of the character, always behind the character, opposite side to the moving direction. It's disabled when the character is on air or isn't moving. Now the ray is somewhat close, so it doesn't add as generous window as some other games do, but it is still there :D It could have been bigger though yeah.