I don't know about the fancy touchscreen stoves.... but my analog Harman P68 has two ways to achieve that feeling.
If you look at the photo I've attached (not my stove), there is a pellet feed adjuster dial 1 - 6, a temperature setting dial, an igniter switch and an on/off/mode dial.
First, I'll say the manual (and my stove dealer) tells you to run it in auto igniter, which warms up the stove, then the stove will shut off when it reaches temperature. When the room demands it the stove will fire back up, but then shut all the way off again when it reaches temperature. If you're not heating a large or poorly insulated area, the stove will get completely cold between runs.
So here are the two ways to achieve the warm wood stove feeling in a P68 (and P43, and probably others too)
1. I use Feed Adjuster 4 (that's the default according to the manual, but it works fine for me), igniter switch down to manual, 75 degrees, and room temp fan on high. With those settings the stove will run the fan on high pushing all the heat into the room, but when the room sensor reaches 75 degrees, the fan will kick off, but the pellets keep trickling in to keep the stove lit. In this mode the stove runs very much like the wood stove I grew up with, except better, because the fan will kick on and off to maintain the room at the specified temperature. If it's a warmish day, I'll run the stove for a couple hours in the morning to warm up the house, then shut the stove completely off until evening. If it's really cold outside it'll just hum along maintaining that specified temperature all day and night (until you run out of pellets).
2. The other way to do this is to flip the dial down to stove temp, and pick a number 1 - 7 instead of a temperature. In this mode the stove will run at the rate you've selected NO MATTER THE TEMPERATURE in the room. You'll constantly have to be playing with the dials if it's warmer or cooler outside, but the stove will be hot and stay hot according to the number setting you've chosen.
It's possible the fancy touchscreen stoves have a similar setting, but I don't have experience with them.