How do I add support blocking for a floating sink (when the wall framing is metal studs)?
You can install wood blocking between metal studs, but you'll have to open up more of the wall to attach them (you obviously can't toe nail them). Notch the block so it fits into the channels in the studs, then just attach it with screws going through the studs.

I wouldn't hang a sink on tile without some sort of additional support.  Even if the tile were strong enough to hold it, it would provide a point of leverage against the wall that could introduce flexing.