Hi Luna,
You aren’t overthinking this.
Stating that they don’t check the dating app often and offering you their phone number instead is just another way to get your number in an attempt to speed the process of communication along.
You shouldn’t simply give away your number because he is divulging his. If you don’t feel comfortable giving that out yet, let him know that.
If he is truly interested in getting to know you, he will respect that and keep communicating with you through the dating app. If he doesn’t, let him go.
This is often a great filter that helps you weed out those who are truly serious about getting to know you and those who are just looking to hook up.