Girl seems interested over text but takes hours to reply

I (19) recently went on a first date with a girl I've known for a while. The date went well and the vibe was good, so I was planning to see her again.

We won't be able to meet for about a month because she's away, but we've still been casually texting. I'm trying to figure out how much interest she actually has.

What confuses me is that she takes several hours to reply almost every time, sometimes 2–4+ hours. But when she does reply, her messages are usually thoughtful rather than dry. She often sends multiple messages, uses “hahaha/haha” and emojis, brings up new topics herself, and asks me questions instead of just answering mine.

For example, I recently replied to her Instagram story with a small joke, and instead of just responding to the joke, she continued the conversation and asked me about the weather . She also remembered a small thing I mentioned during our date and brought it up herself later.

So the confusing part is:

If a girl is interested, but consistently takes hours to reply, how much should I care about the response time?

Does this sound like genuine interest but she's just a slow texter / not glued to her phone, or is she keeping me at a polite distance?

Should I keep occasional contact during the month we're apart, or back off and let her initiate sometimes? And when she's back, should I just ask her out for a second date and judge her interest based on how she responds?

I don't want to play stupid “wait X hours to reply” games, but I also don't want to chase someone who isn't actually interested.

How would you read this situation?