There are currently four games, each having a different storyline.
I didn't really compare them featurewise, it just sounds like something that would happen in one of those games storywise, minus the household appliances attacking you.
But, here are the comparisons.
There are Needed quests, and personal quests. Needed quests are things your character has to get done. Personal quests are things that have to do with nothing special.
Of course, any game will have quests, but Persona has this kind of thing too. Needed quests are usually going through a dungeon meeting a deadline, and personal quests are just, well, personal.
You now have an ingame clock that starts at noon. If you do not progress through quests to help calm yourself and provide a safe environment, you will spontaneously die
In the game, the "Needed quests" I stated earlier will do the same thing. If the player does not meet a condition, such as saving somebody or clearing through a dungeon, your character will spontaneously die. I'm refering more to the 4th game on this one.
Your character is introduced as your average Joe, living a lonely life in a tiny suburban town
Most of the main characters live a normal life as a student at a high school until a certain event happens, just like stated in your description
From getting rid of annoying habits, to getting over fears. You can't do certain quests until you can control your character enough to "persuade" him to do so
In the newer Personas I think, the player will have to change his personality, whether that be courage, knowledge, or sociality.