The way people express their love for each other is naturally different. There are many ways to express love, such as teaching each other things, giving each other gifts, and skinship.
So, when you go out with someone who expresses their love differently, you often wonder if they love you.
Maybe your boyfriend likes to relax with you at home rather than going out, and that is his favorite way to express his love.
The problem here, however, is that although you have expressed your desires to him, he has not responded to your requests.
If both of you actively want to date at home all the time, that's fine, but you're not happy and it makes you feel insecure.
I think it's a good idea to ask your boyfriend why he wants to date and have sex in his room every time more than "because it's calming" and discuss why he doesn't want to go out.
He may not have thought too much about it himself, why he doesn't want to go out. Or he may see you as just an object to have sex with. A sex-only relationship is one thing, but if you don't want to be in that kind of relationship, then of course it won't work.
I think it is better to discuss your mutual desires and move on to a solution. If you have misgivings about the way your relationship should be, it is better to break up.
If he is an indoor person, he may enjoy having tea at a café, staying at home with you, playing games, cooking, or watching his favorite shows.
I think you should suggest what you want to do with him, but if he doesn't listen to your request to go on a date outside, then I think it's natural for you to be worried if he likes you.
Just because you're in a relationship doesn't mean that you want to have sex with him.
Just because you're in a relationship doesn't mean you have to force yourself to have sex that you don't feel comfortable with, and if you don't want to reduce the number of dates or have a relationship that's all about sex, then breaking up is one way to go.
You say that he "won't listen" to you, but do you know what is the reason?
If there's some reason for his physical or mental condition (he's not good at talking to people, his heart pounds and he gets sick when he goes out in crowds, etc.) and it's difficult for him to go out on a regular basis, but if he doesn't seem to listen to you, I feel like he sees you as someone to have sex with rather than a girlfriend.
If you are okay with just having sex with him, then you can continue your relationship with him, but you may not be able to enjoy going out for a movie or dinner with him.
If you feel that you are lonely and don't want to have a sex-only relationship with him, then you will probably feel sad and hurt in the future, so even if you like him, it is better to find someone else who will take care of you and have a good time with you outside.