I hear what you are saying, but I think you need to pull back some. I generally agree with the theory that texting is like a game of tennis in which you have to wait for the other person to hit it back (i.e. contact) you before you reach out again. Certainly there are different circumstances which require different kinds of communication. However, if I send a text like "Hey are you up/around?" and don't get a response I would generally wait until the next day to follow up.
Also, remember the pursuit/distance dynamic. A new relationship is not like dealing with a WW, but many men and women do like both to be pursued, but also to feel like they need to do some of the pursuing themselves. I am dating a woman right now and after 5 dates I was frustrated that it wasn't going anywhere so I pulled way back on communication, basically not texting her unless it was in reply. Very quickly she started reaching and pursuing me as she felt that distance creeping in.
W 34 Me 42 Married 7 years together 8 0 kids 1 beloved dog BD 4/6/2018 I moved out 4/7/2018 I moved back in alone 8/05/2018 I file 3/06/2019 D official 5/7/2019