In 5e, multi classing starts to work against you much quicker than in previous editions. There is almost never a reason to multiclass more than twice, and even that is rare.
You also can't multiclass subclasses, so you can't do a div2/wizard2. It's just a wizard2 who subclasses into div.
I don't know how multiclassing in bg3 works, specifically with scribing scrolls. I know bards who multiclass into wizard can scribe scrolls, but this game doesn't seem to differentiate class spells when it comes to scrolls, so you might be able to scribe wizard spells into your sorcerer book, even though in tabletop you cannot do that. Same idea for clerics, though it should work even less since there is plebty of overlap between sorc and wizard and hardly any between wizard and cleric.
ALSO, you shouldn't have any problem learning lightning bolt as a diviner because you can just pick it as a known spell at lvl 5 div
Does that make sense? I don't know if I covered everything
To test multi bard/wiz I speced into wiz as a bard around level 6 and it gives you separate books; so you can not use bard casts on wiz spells, from what I saw.
In tactical difficulty, I haven't had an issue with AoE as Div Wiz Gale. I use almost every slot on Missiles, Scorching (rarely), and Fireball. I can usually get 3 mobs in a single fireball and 8d6 is huge and only gets better as you upcast is (10d6 fireball is better than 8d8 cone of cold that puts ice in front of you). The item that allows you to cast an extra missile for free really makes it great for level 1 and 2 spell slots, and since they are 100% hit chance, it is great for low hp targets I don't want Lae'Zel wasting a big swing on (like mentioned above).
Counterspell and hold person/monster can be a lifesaver is higher difficulty. Also, putting Haste on Lae'zel makes her have a huge single target burst with action surge. For the end of chapter 2 I used a bunch of summons too, it really sucks that they cant sneak, because they would probably be required spells for me, otherwise.
Div Wiz and a Lore Bard make sure any important saves almost always go in my favor, which is nice. Again, I never use heals, only spells and potions. I kill most everything before it even touches my people, unless it has ranged attacks.
I thought Spirit Guardians were meh for using up a concentrations slot, when I used them, since you have to walk your happy ass over to undead things. I use lightning bolt instead, if it calls for it, since I have a Tempest Cleric. Not finding it useful could be due to my chapter 2 experience though. Since lucky for me, my bard can talk his way out of most things
so in chapter 2 I didn't fight any of the undead lieutenants except for the fat necromancer dude, who I put a antimagic flower on, using pickpocketing.