If your monitor supports FreeSync over a DisplayPort connection (DisplayPort adaptive sync), then adaptive sync will likely work on an Nvidia card as well. You will just need to activate G-Sync in the settings for the monitor in Nvidia's control panel.
A 2060 probably isn't going to be much of an upgrade over Vega 56 in terms of performance though, being less than 10% faster on average in current games. It's arguably more of a side-grade than anything. Power draw, and in turn heat output, should be somewhat lower, but I'm not familiar enough with that Zotac card to know whether it would run cooler or quieter.
You might also consider the Radeon RX 5700, which was released the other day and is typically close to 10% faster than a 2060, though currently only reference models are available, which have a blower-style cooler that runs hot, and partner cards with better coolers probably won't be available until next month. There's also the 5700 XT, which is another 10% faster or so, for about $50 more.