The compatibility thing usually comes down to your wiring, not the age of the furnace itself. A 2010 unit should have standard thermostat wires running to it - most smart thermostats can work with those. Where people run into trouble is if their setup is missing a common wire (the C wire) that powers the thermostat. Without it, some models won't work unless you buy an adapter.
Before you buy anything, pop off your current thermostat and take a photo of the wires behind it. You'll see labeled terminals - usually letters like R, W, Y, G. If you've got at least four wires and ideally a C wire, you're golden. If not, don't panic. Some smart thermostats like Ecobee actually work without a C wire because they have workarounds built in. Nest is pickier about it.
Here's the hack nobody mentions - call your HVAC company or the furnace manufacturer's support line with your model number. Most will tell you straight up if a smart thermostat is compatible, and sometimes they'll even mention which models play nicest with your specific furnace. Saves you from buying something that doesn't work and then dealing with returns. Way easier than guessing based on online compatibility charts.