For my money, 'the Swansea way' has nothing to do with a specific style of football. Laudrup was different to Rodgers was different to Martinez and was planets from Sousa. Plus forgotten Jackett's football of our play off year was just as exciting as any of that but totally different...7-1 vs Brizzle anyone?
No, the real Swansea way that has existed at various times but notably 2007 -2013 is when everyone is absolutely together on and off the pitch, the club feels different and special with no one in it for themselves (even though the lying snakes probably were just pretending, it didn't feel like it), we leverage a point of difference on the pitch - it's not the style, it's the competitive advantage of a different style; we use resources cleverly with superior team building, not just buying players, "splashing the cash" or wasting money on players we don't use. So it was a whole model, not a specific playing style.
Long gone, probably never to return.
Oh and as NJ8 says, it felt the same under Tosh and Struel and the swansea mafia for a few years too. the point of difference on the pitch then was our superb local young players mixed with judicious acquisition of experience.