If I were to multiclass Sorcerer 9 Bard 1, could I use an instrument (per Bard Level 1 feature) as my focus for spells that appear on both class spell lists?
For example, Polymorph, Confusion, and Hypnotic Pattern all appear on both lists. Can I use an instrument focus for these if I know them as Sorcerer spells?
No.
Under the rules for the spellcasting class feature of multiclass characters, this is explicitly covered (PHB, p. 164; emphases mine):
Each spell you know and prepare is associated with one of your classes, and you use the spellcasting ability of that class when you cast the spell. Similarly, a spellcasting focus, such as a holy symbol, can be used only for the spells from the class associated with that focus.
But note that a multiclass spellcaster can use a component pouch to cast spells from all their classes:
A character can use a component pouch or a spellcasting focus ... in place of the [material] components specified for a spell.
(PHB p. 203)
No, you cannot. The Bard's spellcasting focus feature says you can use a musical instrument as a spellcasting focus for your Bard spells. This does not extend to spells that you may cast that are granted to you by other classes. This means that you could only use the instrument for spells that are on your spells known list from your bard levels.
Spellcasting Focus
You can use a musical instrument (see chapter 5, “Equipment”) as a spellcasting focus for your bard spells. (D&D 5e SRD, published under OGL)
