Zardnaar
Legend
The rules are that if you have a focus in hand you can use it for the M component and use the same hand holding the focus for the S component.
The problem most caster have is this doesn't work for S components if there is no M component. So most caster need Warcaster to cast Shield I'd they have their hands full even if one of them is their focus (ie Focus works for VM and VSM spells but not VS or S spells)
This is not the case with Artificers because they add the M component to ALL spells for them. So having a Focus in their hand (say an infused weapon) let's them do both the S and M component. They don't need Warcaster to cast Shield if one of their hands is holding a focus.
Point except you explained it slightly convoluted.
M part is still irrelevant in regards to the focus as it was the S part tripping up.
If you infuse a weapon or shield you can essentially ignore the S part and still fight vs pure spellcaster artificer not bothering with full hands.
Checked 3 sections in two different books mein gott 5E layout.