I define full vs half caster based primarily on the maximum spell levels they get (warlock is full caster because of mystic progression), and secondarily on when they get access to the next spell level (generally every second level for full casters). Other people define it differently, and they are wrong...er I mean, it's discussing apples and oranges to not clarify their definition.
Making full casters into half casters as defined above would necessitate giving them very castery feeling features that are mechanically balanced with the non-casting features of the existing half casters.
Artificer already sort of does that.
If you want something that feels like a wizard or sorcerer you would probably need to give them a lot more oomph. Taking a page from 2024 monster design, you should increase the damage of their at-will cantrips to be competitive with their slotted spells (maybe they get a feature that just says their cantrips do double damage or otherwise have double effect). Leave their limited spell slots for increased utility (combat and non-combat) and let them having excellent DPR with cantrips. Instead of buffing cantrips (or as a supplement, since otherwise you would obsolete cantrips), you might just give them unique damage blasts features, like the NPC casters in revised monster design.
Giving them more lower level slots would be okay, if you don't mind fundamentally changing mostly standardized tables. If you want to keep with the general design though, you should avoid that and instead give them other ways to get more spells. I'd recommend allowing certain 1st-level spells (and possibly 2nd-level) to become at-will.
Also play around with rituals to make them more easily available. Maybe full casters don't have to prepare them, and wizards have the added benefit of being able to cast them faster and/or cast certain prepared non-rituals as rituals.
If you want them to have access to higher level non-combat utility magic, like teleporting, plane-shifting, etc (which to me is fundamental to what a D&D wizard is all about), you need to give them unique rituals allowing them to access that stuff, like 4e, but restrict those to the full caster classes, and probably certain levels. Make them require expensive consumables. You need a full caster to be able to use them, but they fundamentally switch from a character power to a party ability at that point.
Finally, you want to give them some special abilities that are evocative of their focus on magic. You need different ones for each class to fit the theme. Make sure they still feel like they are much more focused on magic than a paladin or ranger. They keep worse HD and armor/weapon proficiencies.
Overall, you need more quantity and power in spells as well as alternative damage scaling and additional features, and optionally a way to access higher level magical utility abilities, if you are cutting them down to half caster and still want them to maintain a full-caster relative feel.
