Perhaps he gets unstuck when he realizes a key detail or remembers a forgotten solution. Maybe it's a combination of physical effort and a sudden inspiration.
He might use his magic skills. For instance, he could use a spell to break whatever force is keeping him in the middle position.
One way is to wait for the object his tongue is stuck to warm up a bit. If it's a metal pole, for example, as the surrounding air temperature rises or if the sun shines on it, it might gradually warm up and his tongue will come loose. Another option is to breathe warm air on it. He can cup his hands around his mouth and blow warm air towards his tongue. This might take some time but could work.
If she's stuck in a physical space like a small hole or a tight corner, she can try to wiggle her body slowly. Sometimes a little movement at a time can help her get free.
She could try to wiggle her way out gently. If it's just a matter of being a bit wedged, some careful movement might free her.
She can try to gently twist and turn her foot to loosen it from whatever it's stuck in.
Maybe someone pushed her from behind to get her through. Or pulled her from the other side.
Try using a thin object like a ruler or a wire to carefully push the manga out.
The OC could use its own unique abilities or traits. If it has some special magical power that hasn't been fully utilized yet, it can be the key to getting unstuck. For instance, if the OC has the ability to communicate with magical creatures, it could ask a helpful creature for assistance in getting out of the difficult situation in the fanfic.
One way is to set a limit on your reading time. For example, decide that you'll only read Percy Jackson fanfiction for an hour a day. This can help you break the cycle of being constantly immersed in it.
One way is to limit the time spent on it. Set a timer when reading or writing fanfiction and when it goes off, move on to something else.