I mean if you multiclass so that you have the proficiency from another class.
Like a fighter splash, for example.
Even if you are a multiclass wizard with shield proficiency, you still can’t cast spells while holding a shield.
I don't think this is correct, at least in 5e. Are you basing this off of your understanding of 5e rules or BG3's implementations?
As I understand it, Wizards in 5e don't have any restrictions on casting besides the need to have one free hand when casting spells with Somatic and/or Material components. If they gain shield (or armor) proficiency, then can wield/wear those just fine, as long as their other hand is free or holding a Spell Focus.
Hexblades, for example, gain proficiency in shields but nothing else specifically that says "in contrast to other spellcasters, you can cast while wielding a shield."
You are correct, however, that a spellcaster cannot wield a weapon in one hand and a shield in another hand and still cast spells. (However, 5e RAW they could drop the weapon, cast the spell, and then pick up the weapon. And in BG3 they could swap to their bow, cast the spell, then swap back)
