In official lore, what magic is forbidden in Strixhaven

In Forgotten Realms lore, manipulation of magic is done through the Weave. The 5e interpretation of this is shown on pg. 206 in the side bar "The Weave of Magic".

[Mortals] make use of a fabric of magic, a kind of interface between the will of a spellcaster and the stuff of raw magic. The spellcasters of the Forgotten Realms call it the Weave and recognize its essence as the goddess Mystra, but casters have varied ways of naming and visualizing this interface.

Whenever a magic effect is created, the threads of the Weave intertwine, twist, and fold to make the effect possible.

Under "Known and Prepared Spells" on pg. 201:

Before a spellcaster can use a spell, he or she must have the spell firmly fixed in mind, or must have access to the spell in a magic item. Members of a few classes, including bards and sorcerers, have a limited list of spells they know that are always fixed in mind. The same thing is true of many magic-using monsters. Other spellcasters, such as clerics and wizards undergo a process of preparing spells.

Spell Slots represent the physical and mental exhaustion created by casting these spells (PHB 201, "Spell Slots"), which is why you can only cast so many spells between rests with the exception of cantrips, described as easier spells that are second nature to a caster.

Wizards differ from other spellcasting classes in that they completely study the Weave in a very scientific way. As you stated in your question, Wizards prepare their spells by fixing a certain number of spells from their spellbook in their mind for use during the day. The number of which is determined by a mix of the Wizard's intelligence and their study in the class (PHB 114). Wizards have a very wide array of spells at their disposal because they are masters of documenting the arcane. Other classes learn spells through a higher being or by practicing the physical aspect. Wizards are the only class in this edition who keep vast physical research notes to allow them to recreate not only spells they have experimented with but spells found on scrolls or other tomes.

In general, you're going to be hard pressed to find a very large area where magic does not function or is entirely forbidden, for the simple fact that D&D's adventurers have always been highly magical and dependent on magic. A place where none of your cool stuff works anymore or where several character classes become almost entirely useless is not likely to be a fun place to set adventures, so they aren't going to take up much space in a published setting; places where the rules of magic are just a bit different are more common.

If you're happy to operate at a very small scale, though, there's a couple of spots in the Forgotten Realms which you might look into. FR is normally an extremely high-magic setting and the dead-magic zones which do exist are not large enough to fit an entire kingdom in by any stretch, but there are:

The City of Tantras

During the events of the Time of Troubles, the gods Torm and Bane fought each other in the city, the end result of which being that the gods slew each other and the battle created a dead magic zone covering the entire northern quarter of the city ("a zone of some 400 acres", apparently).

The rest of the city still has magic, and the dead magic zone itself isn't a pleasant place to go as it became widely used by criminals hiding from magical detection.

The Valley/Village of Dead Tree Hollow

The valley now known as Dead Tree Hollow was turned into a dead magic zone a few hundred years ago, after a vengeful mage furious at being rejected instead decided to murder the unfortunate lady and everyone around her.

The valley is small, but large enough that it contains a small village and surrounding lands, so it could be suitable as a no-magic location for small-scale adventuring. Note that even in this case it's not as if magic will be unknown to the villagers that live there - they would not have to travel very far to find places full of wizards and clerics.