Why doesn't "campaign" have the meaning of "countryside" in English?

British (and American) senior officers were mostly educated men fluent in French and tended to (out of snobbishness) use French military terms: enfilade, siege, cavalry (chivalry) , fusilier, dragoon, grenadier etc. etc. so Campaign was just in a long list of French military terms taken wholesale into English.

Farmers on the other hand who were less educated and closer to their Anglo/Saxon/Nordic heritage favored words with Germanic roots, field, cow, hen, meadow etc.. Pasture is about the only agricultural term I can think of that doesn't have Germanic roots.

Campaign was used to mean ‘a tract of open country’ until at least the middle of the eighteenth century. The process by which a word widens its meaning can be described as ‘extension’ or ‘generalization’, although in the case of campaign the earlier meaning has been lost.

Doubtless ‘extension’ or ‘generalization’, ‘development’ or ‘evolution’ fit the process you describe, and I suggest ‘campaign’ isn’t an example.

https://www.collinsdictionary.com/dictionary/french-english/campagne for one, supports my belief that ‘campagne’ no more means ‘battle ‘ in French than ‘campaign’ does in English. In either language a campaign is the series of battles that make up a war, and could mean ‘(a) battle’ only if by co-incidence the whole issue happened to be decided in a single fight. A campaign doesn’t have to include even one battle. It might be rare but campaigns and wars are best won by manoeuvre, not by blood-letting, which is why to go ‘on campaign’ means to take to the fields. It includes the readiness to accept a fight but it’s in the field, not the fight that we find the essence of the thing.

Almost identical etymology calls people who take their holidays under canvass ‘campers’ and explains both why demonstrators might ‘camp on your lawn’ and why that’s not quite the same as ‘parking their tanks on your lawn.’

The ‘countryside’ meaning might be lost in some dialects; it certainly isn’t in broad English.

Where I live in rural Suffolk, sugar beet farmers frequently say ‘campaign’ where other folk would use ‘harvest’, rather clearly meaning ‘to go to the fields and do all those beety, farmy, harvesty things that we do there at this time of year.’

I suggest - with no specific research - that the real derivation of commercial or political ‘campaign’ is not to battle for sales or votes, but simply to go out into the field…