If you have smoke/ash dust in your house you have draft issues.
Not necessarily.
I use a PM sensor and it shows slightly elevated PM when the stove is on. There far more PM when frying something, and its off the charts when you vaccum.
we have a major dust problem with our half dozen golden retrievers bringing in dust and horsing around in the house.
Our wood burning insert creates a lot of dust and every now and then a wood burning smell
There are a lot of sources of dust in a house. I don't know the source of the OP's dust, but the following may help if it's ash dust from the stove.
Lydiae, what brand and model insert do you have? How are you removing the ash..using the insert's ash dump, or shoveling the ash out? If you use the ash dump, can you describe it in detail?
If the stove has a poor ash-handling system, and you're forced to shovel it out, there are a few ways to minimize the amount of dust that escapes.
Remove ash only when it's cold outside, draft is strong, and it is pulling any dust created back into the stove well.
Slide shovels-full of ash off into the bottom of a
long, shallow pan, by tilting the shovel handle up and moving the shovel nose along the floor of the pan.
Don't haphazardly dump shovels full into a deep bucket..that creates huge clouds of dust, and the draft might not be able to catch it all.
In this pic, the pan is on a box, which I wouldn't do. If I were actually cleaning out this stove, I'd be holding the pan directly under the door, as close as possible, with my right hand and I'd be operating the shovel with my left hand. Or I'd get a load of ash on the shovel with my right hand, then set it in the stove for a second while I switched hands.
Shoveling out an insert or a front-loading stove, you might need to let the coals burn out so you don't get roasted. It might not be as easy to position the pan under the door, and draft might not be as strong as it is through the smaller side door shown here.
I don't enjoy cleaning out ash so I generally get stoves with a grate in the floor. All I have to do then is swirl a poker through the ash, and it falls through the grate, leaving all the coals and any dust inside the stove. I can leave as much or as little ash as I want in the stove.
The Buck 91 had a good ash dump, with a large opening, better than 3"x5", on the left side of the floor, and a hinged lid.
The T5's dump would be OK with a bigger opening.