It seems like you should be able to make the call on what people should expect wrt your responsiveness.
I definitely know for most of my friends how they are responsive in what situation and I'm fine with their different rules. I expect them the same for me. Never told them but I have not had issues so far.
Just answer however you feel like doing this and people will have no choice to catch up anyway. It's probably fine to take hours or even wait the next day to answer a text. If someone asks you can tell them. If you feel pressure from message (notifications) to answer, that's probably something you can learn to manage and let go.
I know few people who actually expect others to be able to answer fast any time. I'm quite responsive myself usually but I fully expect most of my friends to answer in a few hours or even the next day, and if they answer fast, that's neat but not expected. Some friends take days to answer, I adapt. If they miss something, their loss at the end, but usually I think they see the message quite fast so that does not happen. If I propose something to a friend who usually answers the last minute and something else come up, I consider I can cancel with this last minute friend so I don't let their rules eat me neither.
Don't let the phone or the computer control you. That should be the reverse. If you are spending time with someone or watching a movie, just don't check out your phone. Put it away. It's going to be fine. If anything urgent happens they will call. Tell them if it's not clear for them. I do not answer non urgent stuff when I'm actually with other people in real life. They have priority. That allows me to enjoy and focus on them better. Messaging stays asynchronous and that's how it's designed.
Life is so enjoyable this way.