I sweep at least once a year, usually twice: Summer/fall, and if we get a warm spell in mid-winter. I use one of these and have had good results:
https://www.amazon.com/dp/B085GCN5KP?th=1
I use it from the stove side, put the drill on slow speed, and work it up and down on each length, then add another rod, etc. Same thing on the way down. It's a little messy, but not too bad. You can have your shop vac hose inside the stove with the door only open as much as needed and it keeps the dust down to a minimum. You might be surprised how much junk comes out and you'll definitely feel better about it afterwards!
I assume you have a baffle so you'll need to remove it and make sure you cover the air pipe/manifold in the back of the stove with duct tape or something to prevent crap from getting in there. There's also probably a gasket there. Inspect/replace it if needed.