Interested but cautious

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What you described suggests real interest, and also real caution. They might be cautious because they are coming out of a painful breakup, because they have an avoidant attachment style, because they are unsure what they want long-term, or because something about you or the situation feels unfinished to them. None of these are necessarily dealbreakers. But the most common mistake at this stage is to chase, which usually makes cautious people more cautious. The second most common mistake is to assume their slow pace means they are about to pull the rug out. It often does not.

What to do next

Let them come to you more than you come to them for the next two weeks, without playing games. Just live your life. Notice whether their interest continues to grow on its own, or whether without your pursuing, it fades. Both answers are useful. Resist the urge to demand certainty before they are ready to give it.