People have been preserving food with smoke, likely since before agriculture. More recently phenols in wood smoke have been shown to have antimicrobial and antifungal properties. Eg: https://pubmed.ncbi.nlm.nih.gov/37152755/
Stands to reason that any culture which smokes food to preserve it might try fumigating with it
Treatment of food by smoke is done before a pathogen has a chance to proliferate.
If a fungus sets into wood, and smoke treatment is done after the fact, the smoke won’t be able to penetrate deep enough to completely eradicate something that’s well established.
Stands to reason that any culture which smokes food to preserve it might try fumigating with it