No, you do not have to purchase the latest version and can use your acquired PaperOffice at no extra cost.
Please note that the updates included in the USP are always valid only for the current version. This means that you will NOT receive updates for an outdated version.
Please note in addition that the database compatibility is guaranteed only to the previous version, e.g. an update from version 2019 to version 2020 would be possible as the database structure is automatically adjusted to the changes.
In a cross update (for example 2015 and 2019) an automated data transfer is not guaranteed. In such a case, contact support to consider manual data migration (paid service).