Hi James,
If you are always the one who initiates conversation and she sometimes takes 1-2 days to text back, she doesn’t like you wholeheartedly.
She doesn’t think of you as much of a priority.
When she has nothing else planned, she has been fine with going out on a date with you.
She is attracted enough to you that she has paid for the two dates that you have been on, given you a gift on the last one and invited you back to her place to Netflix and stuff.
However, once she is done with the date, she is not thinking about you all that much.
This is why she left your message on read when you thanked her for the day.
You should not keep pursuing her.
She has been interacting with you for the last month.
That is more than enough time for her to know whether she is into you or not.
Her behavior so far has shown that she is very lukewarm when it comes to you.
She would not be someone worth pursuing any longer.