No, if you purchased version 1, you can keep using it permanently. You do not need to purchase a license for Version 2.
Artisan version 1 (1.3.7) is currently compatible with SketchUp Pro 2017 through 2023. As long as you have a license for one of those SketchUp versions, we expect that you will be able to keep using Artisan v1.
However, Artisan version 1 licenses will no longer be sold or supported and we cannot guarantee compatibility of version 1 with future versions of SketchUp.