Girl takes long to text but is very invested in person?

This is my first situationship after my first rl ended 2 years ago, im rather inexperienced in the dating scene.

Been seeing a girl for around 7-9 dates within 2 weeks its going very well. Already stayed a night over at my house. What bothers me tho, its always me taking the initiative to meet up. she's always cooperative when planning a date and in person she is all over me but I hate that I always have to be the one to text her or I won't hear from her for over 8 hours and maybe more if I probably would stop texting.

Ik she's at her phone often from when we are with friends. Checking whatsapp and insta regulary from time to time.

I have interest in her obviously and know she's a bit insecure as she told me she had really bad luck in dating in the past 3 years as men kept ghosting/dropping her but now I feel like I am investing way to much or is that to be expected of a man? Its just strange bec my ex was always texting me so much that it was often to much and this girl barely sends me 1-2 sentences a day.

Is this some sort of stupid game, bec if I already start to feel a bit tired of it. Should I just stop texting the next time after a date until she is the first to respond? I feel like I am doing way to much and should maybe show less interest?
Girl takes long to text but is very invested in person?
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