No, because FreeSync 2 was retired. As the games industry evolves and changes, so do the technologies that enable gaming and gamers. AMD completely revised FreeSync branding and features in late 2019. Instead of two layers, basic FreeSync and FreeSync 2, we now have three tiers. Baseline FreeSync remains the same, focusing on screen tearing (or variable refresh rate, based on VESA Adaptive Sync). The new tiers, FreeSync Premium and FreeSync Premium Pro, rose from demand for high framerates. Both were designed with a minimum of 120Hz in mind, whereas original FreeSync from 2014 was developed in an era when 60Hz was quite fast. The two top FreeSync tiers further add low framerate compensation to prevent refresh rate dips due to heavy performance loads in-game, especially in framerate-centric titles like first person shooters.
Only FreeSync Premium Pro supports HDR at the moment. While nominally all versions of FreeSync don’t cost manufacturers anything in the form of royalties, of course technical complexity increases as we go up the tiers. So a monitor with entry-level FreeSync will likely cost less than one with FreeSync Premium. But if you want HDR and FreeSync together, make sure the specs say FreeSync Premium Pro and that the technology’s logo appears somewhere in materials related to the monitor you’re buying.