How to prevent a context class using the state design pattern from having too many responsibilities?

I am making use of the state design pattern for a project of mine where I have a Car class which is the context class and it can have 3 states - neutral, drive and park. In each of those states, the car can execute different actions such as in Neutral, you can play a movie in the car, in Drive you can do something else and in Parked as well.

Now, I can see the benefits of the state design pattern, not using too many if statements and keeping logic separate for each state and making it easily extensible code but after some thinking I am not sure how to prevent the Context class from having way too many responsibilities. At the moment I have just a few actions but in the future I might want to add like 5-6 actions per different state and then my Context class will be full, in addition to keeping track of the speed of the car, fuel etc.

First of all, is that a problem and second, if yes how to prevent that?

I tried researching online but could not see any articles on the Context class having too many responsibilities which led me to thinking that maybe this is normal but still I am not completely sure.