The main 3D Warehouse window, or going there in a browser, doesn’t support 2016 (other than you can download Collada. You could let us try the one that failed for you). But, in the Components panel in SketchUp you are shown models that are compatible with your version. You could search in their for what you want, and 2016 will be shown most of the ones that 2019 is shown.
As I understand it, models made for any version are kept in their original format, and also converted to the three most recent versions. A model uploaded as 2019 would be available to someone using 2017, but not 2016. A model uploaded as 2017 would be available in a year from now, and also converted to 2020, 2019, and 2018.