The *Immediate" diagnostic is a Manometer to measure draft, but you don't seem to have one installed so we won't dwell on that.
I have a " new to me" 25 year old Haas and Sohn stove, hearth mounted.
I first fired my stove last night, and everything went like clockwork. Before I lit the stove, and before I would light any fireplace, I check the draft by lighting a piece of newspaper to see there is some draft present.
On my top-loading stove, before I even tried lighting the newspaper, I checked draft by opening the top loading door holding an incense stick a few inches over the open door and watched as the smoke was drawn down into the stove. Then I did the newspaper thing...OK looks good (mind you, two days ago I could look up and see that the flue was clear, and it WAS a working fireplace.) I put my paper, kindling and charcoal in place then soon added coal (nut) to the hot bed...and "Bob's yer' Uncle" ...
My draft settled to .05" water on my Dwyer Manometer, with adjusted stove & baro-damper...Cake!
It all went as expected. Before hand, I had check out some of the variables, that others on the site had experienced, causing failure...Chimney and draft are number one. A tight stove is next. I tried to knock-out the common pitfalls before I lit anything [I would have hated to have to unload a stove full of half burnt coal]
Draft? Check as able ...
Maybe close your manual damper, open your baro-damper by hand and see if smoke from a cigarette, cigar, smoky wick, incense stick or (what have you) might be drawn to the baro-damper opening... Rely simply on the pressure differential of room temperature air and outside air. (cool stove, obviously)
Then try the opening the manual damper and see if you can get draft from lighting paper in your stove, about one sheet at a time.