What would the society be like in such a fantastical country?

The society would be a magocracy but unless it had industrialisation it would not have universal education. Universal education was development to support industrialisation. A magocracy would be very conservative and classist and likely have some process of forcibly inducting sorcerous children into the state service.
The degree that this would not be the case, would depend on the nature of divine and primal magic and the general attitude of the gods on the matter.
 

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More likely would persecute them. Sorcerery cannot be controlled and as such is a direct challenge to the Magocracy control just by being impossible to gatekeep.
There is no need for that if you can grab them young and indoctrinate then into your system. See the Janissaries, or the Mamelukes
 

3e magic is more capable than 5e while adventuring, but 5e magic is more impactful to the society. The 3e cantrips don't last long, can't be cast often at low levels, and at low levels have minor effects, while 5e cantrips can last 1 hour, can be cast infinity times, and have meaningful impact. This inverts at the upper levels.

But 3e magic is effective militarily. 3e humans can get scribe scrolls at 1st level and at 4th start making wondrous items.

Scrolls mean those few slots per day can be augmented in times of need, allowing a bunch of utterly forgettable apprentice-types to make many +1 weapons for troops or to use True Strike with heavy crossbows to unleash a lethal volley at extreme range. Heck, a literal "shield wall", that can provide cover for troops behind them.

At 4th level, when they get a feat, you add Wondrous items. Even the most minor ones will add up for the military. Horseshoes of speed or Zephyr for the cavalry, boots of levitation for scouts, goggles of night, horns of fog/bottles of smoke to provide cover, slippers of spider climb, pipes of haunting as a reusable way to break up enemy forces.

But the lowest level 3e spells just aren't that useful in normal life.

5e cantrips & 1st levels are world changers.
 

3e magic is more capable than 5e while adventuring, but 5e magic is more impactful to the society. The 3e cantrips don't last long, can't be cast often at low levels, and at low levels have minor effects, while 5e cantrips can last 1 hour, can be cast infinity times, and have meaningful impact. This inverts at the upper levels.

But 3e magic is effective militarily. 3e humans can get scribe scrolls at 1st level and at 4th start making wondrous items.

Scrolls mean those few slots per day can be augmented in times of need, allowing a bunch of utterly forgettable apprentice-types to make many +1 weapons for troops or to use True Strike with heavy crossbows to unleash a lethal volley at extreme range. Heck, a literal "shield wall", that can provide cover for troops behind them.

At 4th level, when they get a feat, you add Wondrous items. Even the most minor ones will add up for the military. Horseshoes of speed or Zephyr for the cavalry, boots of levitation for scouts, goggles of night, horns of fog/bottles of smoke to provide cover, slippers of spider climb, pipes of haunting as a reusable way to break up enemy forces.

But the lowest level 3e spells just aren't that useful in normal life.

5e cantrips & 1st levels are world changers.
Unfortunately, the cost of making (and indeed mass-producing) magic items is prohibitive. Even producing goggles of night will cost 6000 gp and 480 XP from a 3rd level caster with the right Feat, working over 6 days. Of these, the money is probably the most limiting - 6000 gp is the annual income of 100 skilled artisans, or the cost of four suits of full plate armour, basically the annual economic output of an entire small town. But even if the money is forthcoming, I don’t imagine the artificer is keen to give up 480 XP without significant recompense - the full cost of the item, in other words, or 12 000 gp. It’s like having a war economy based on mass-producing Mona Lisas.
 

- the full cost of the item, in other words, or 12 000 gp. It’s like having a war economy based on mass-producing Mona Lisas.

First off, a 4th level character in 3e would have wealth around 5,500gp. Perhaps in this world that is their profit for making the goggles. 12k -6k = 6k profit.

However I would posit that mages are taxed in XP. Only the mundane pay taxes in gold. The government uses the gold from the many mundanes to provide the materials (6k gp worth for goggles) and the mage has to spend their XP. If the Duchy is providing access to spellbooks and such, its only fair.

Since attunement isn't a thing in 3e, items can be readily shared and swapped between troops. Does every soldier have super-expensive night vision? No, but certain details will have them. They accrue over time

Spies would have ready access to hats of disguise (1,800gp) and hand of the mage (900gp), brooches of shielding for nobility (1,500gp), and the various elixers, ungents, and oils.

You brought up the mona lisa. Ungents of Timelessness (150gp) can cover many paintings and cause them to age 365x slower than normal. You could make masterwork equipment ignore the ravages of time for less than 20gp ea. 10gp if it is bought at "wholesale" prices via taxation.
 

First off, a 4th level character in 3e would have wealth around 5,500gp. Perhaps in this world that is their profit for making the goggles. 12k -6k = 6k profit.

However I would posit that mages are taxed in XP. Only the mundane pay taxes in gold. The government uses the gold from the many mundanes to provide the materials (6k gp worth for goggles) and the mage has to spend their XP. If the Duchy is providing access to spellbooks and such, its only fair.

Since attunement isn't a thing in 3e, items can be readily shared and swapped between troops. Does every soldier have super-expensive night vision? No, but certain details will have them. They accrue over time

Spies would have ready access to hats of disguise (1,800gp) and hand of the mage (900gp), brooches of shielding for nobility (1,500gp), and the various elixers, ungents, and oils.

You brought up the mona lisa. Ungents of Timelessness (150gp) can cover many paintings and cause them to age 365x slower than normal. You could make masterwork equipment ignore the ravages of time for less than 20gp ea. 10gp if it is bought at "wholesale" prices via taxation.
My point about the Mona Lisa is really that in the setting, magic items are so expensive that only the very wealthiest in society can afford to commission or buy them. They’re more like unique priceless works of art than military equipment. Even if this magocratic government devoted a massive amount of their economic output to buying magic items, they wouldn’t be able to produce enough to make much difference in a war scenario. Maybe over a century or two, if they stockpiled and inherited items (and the items still worked after a century). That’s just using 3E rules, as noted by the OP.

(Note that unless you’re somehow magically summoning gold (and then hello inflation) or digging it regularly out of dragon hoards and dungeons (ditto) the kingdom only has as much cash as it can trade for, and the basic rules of economics apply. Our mostly agrarian kingdom of a few million people would be lucky to have an annual GDP of more than about 10 million gp, of which at best maybe 20% would be available for government spending. That sounds like a lot (2m gp), but I assume we’re planning to pay all our highly trained wizard soldiers something, probably at least 1000 gp a year each (1000 wizards = 1m gp) not to mention buying weapons and other equipment, paying other staff, maintaining buildings and roads, etc. Our magical item project is going to have to compete with a lot of other much more essential budget items.)

(Basic benchmark: the going rate for a skilled artisan in 3E rules is about 5sp a day, which means their annual gross income is about 125gp.)

So a magical Industrial Revolution - which is what you really need to boost this kingdom’s magical military capabilities, much as you need to boost any of their capabilities, be it educational or agricultural or whatever - is also off the cards. The only way to work it is to bring in a specific 3E supplement and make Eberron rules apply. Artificers and magewrights make all of this possible, if not likely.
 
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