No, Caato Time Tracker 2 uses a new subscription model and previous licenses can't be converted. Having said that, please watch out for announcements in CTT 1/+ apps, there will be discounts available for existing Pro users.

Prices vary by country, you can see pricing either by downloading the app or at the end of the app store description.

Most likely you have a date filter set at the top of the app that excludes previously tracked times, please reset the date filter to "All time entries".