I think that’s a bit strong: I wouldn’t call Myr the “workshop of the world.” It’s somewhat more diversified, but not that much more. Yes, they have optics, weaponry, fine woolens, lace, glassworks and tapestries….
But Qohor has metalworking on lockdown, Tyrosh has dyemaking and distillation (which suggests chemistry) and competes with Myr on armaments, Lys is a competitor in the tapestries business and has a better chemicals industry, Norvos is a competitor in the tapestries business, Braavos dominates in finance and is the only place that’s figures out the assembly line and interchangeable parts.
So I would say that the Free Cities are fairly even when it comes to industrial development.