Have you looked at One Page Rules' "Age of Fantasy Regiments" at all?
It's pretty good in terms of providing framework for you to add your own story narrative to, and whilst the rules are streamlined they still produce challenging games with interesting decisions. This is good if you're paying solo, as it means less for you to hold in your head or need to refer to when playing. And virtually everything you need to get started is free...
Link. There is also a skirmish version "Age of Fantasy Skirmish", which would allow you to intersperse bigger battle battle games with small commando-style missions:
Link.

Are there any decent campaign rules, supplements, with a focus on narrative? Be it generic or at least loosely tied to a setting. Somewhere between an RPG sourcebook and the usual back of the book into to fighting linked games.
Less to do with saying the winner of a battle gets +1 attack for a character or army gets a re-roll next game.
Well, unless the scenarios are pre-linked to each other in a tree structure, where the outcome of each battle directly affects the next (including bonuses and penalties), most campaign systems will be more along the lines of what you've posted in that units get small modifiers as a result of the games they participate in. I mean... There's not too much more that can really be done without substantially more complex rules.
Of course, it depends on how you interpret the results that really matters IMO; that +1 to ranged hits could be that your army has found or captured a superior store of ammunition/weapons, or that a legendary marksmen has agreed to help you by helping to train some of your troops, or it could be a temporary bonus to reflect the unit being rested/morale-boosted/in a superior tactical position/weather. That's up to you to interpret in a way that makes sense for the games you're playing.
GW did some fun sets during 5th Warhammer, but they were very tied to a structured story and the armies featured. Age of Sigmar ones are fun to read, but very tied to the armies and named characters.
My recollections of the WHFB 4E/5E campaign supplements is a little different! Namely:
1) The "historical" armies in the supplements were often rather odd, with troop types/numbers that didn't seem to fit the collections of anybody I ever knew. For example, something like needing 35 Dark Elf Scouts for just one scenario, when nobody I knew ever had more then 10 (if indeed any at all, since there were no models released for them that during that edition!). Whilst I often felt this was to encourage players to try new things, I also always got the sneaking suspicion that this was also to boost sales of less-popular or less well-selling figures. Cynical, I know!

I believe most people got around this by just proxying the units they didn't have - for example using Warrior and Corsair models for Scouts.
2) There was always the option of using the parameters for choosing your own troops for each scenario, so that you could make selections more based on what you owned. I think this is how most people built their forces for the scenarios.
3) There were often suggestions on using different armies for the campaigns, and how the campaigns/scenarios could be "re-skinned" to suit possible different stories. Honestly, I often wish these sections were a touch more fleshed out, but I can understand why they weren't
So, if you liked a campaign supplement from the above, but wanted a different narrative, you could easily do that. For example, in Idol of Gork, the Orks could be swapped out for Lizardmen, the Empire for Dark Elves, and the whole campaign set in Lustria instead. Very little would then need to be tweaked to fit the new story, and the missions are all interlinked still. Your ability do this has never really been taken away from you!

Failing that, what's the most useful back of the rulebook campaign? I have Oathmark as an example, that felt more just winning territories that affect your army choices.
Again, this is fairly typical/common? Most historical battles were fought for territory and/or power after all... In your games, it's up to you to interpret what the gains actually mean. The new territories could represent raw conquest, or they could represent building alliances and/or assisting other kingdoms in return for their support when you need it. Similarly, the troop types the territory unlocks for you could be interpreted (voluntarily) by you on different ways - for example, being able to include more Human Linebreakers could reflect an upgrade of your regular units in training/equipment/etc instead, and you could voluntarily opt to swap regular infantry for Linebreakers to reflect this (i.e., through gaining more territory benefits, you can change the composition of your forces, rather than just adding more options to what you already have).
I think that in all cases, what you're after is narrative framework rather than campaign rules as such. The more game agnostic or generic these become though, the more they get reduced to mere "Unit X gains +1 to hit" in the post-battle.
I also think it's important to try different scenarios, and to try deliberately unbalancing them as well. The "win" in such unbalanced scenarios can then be changed to reflect this. For example, you could play a Last Stand type scenario, but with extremely lopsided forces; the disadvantaged side's victory is then how long they hold out or how quickly they defeat the other side. That time period is what could then have an effect on your next scenario (for you to determine). It could mean that in your next game one side gains/loses units or troops in units, or they suffer a penalty, or they get some other appropriate benefit/penalty (perhaps the unit arrives late or early, or starts dug-in, or can be re-deployed before the first turn, or gains a free move, or...).
Finally, there is a WW2 supplement published by Too Fat Lardies called "Platoon Forward" that might interest you from a structural point of view (link to chat-through
here). In this publication, units and their leaders all have different personalties, abilities, quirks, etc. This all affect their interaction with you, and with how likely they are to do what you want them to in game. Post-game results gradually change/add to these characteristics, and the system as whole in intended to be played solo. I don't see why the system can't be adapted to whatever setting you wish.