RAW, Wizards can copy any spell that they can prepare into their spellbook once the requisite prep has been done. But if you have, say, an 18th-level Artificer with 2 levels in Wizard, the multiclass allows you to cast spells up to 6th level... and the Wizard spell manager still only allows you to put 1st level spells into your book.

Upcasting is all well and good, but one of the perks of the Wizard class is the ability to fill your spellbook to increase versatility. If I have a 6th level slot, why can I not copy a 6th level spell?

Because to copy a spell into your Wizard spell book it must be of a level you can prepare:

Copying a Spell into the Book. When you find a wizard spell of 1st level or higher, you can add it to your spellbook if it is of a spell level you can prepare and if you can spare the time to decipher and copy it.

When it comes to multiclassing the Multiclassing Spellcasting rules explicitly say:

Spells Known and Prepared. You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of that class.

So your level 2 Wizard can still only prepare 1st level spells.

Oh! Okay, yeah, my mistake. I didn't see that part of the multiclassing rules. Thanks.