You're correct, it won't work well with 10.15, since it is a few major versions out of date. The Apple App Store does not offer upgrade pricing, so you have two options:
Just buy Camtasia 2019 via the Apple App Store. This will give you a license for Mac only.
Upgrade with us directly: Contact our customer service department, provide proof of purchase from the App Store (your receipt from Apple), and get upgrade pricing. This license would be for Mac OR Windows (combined license)