Does anyone know why the barrel is so loose when the slide is racked? And is this normal? Any cause for concern?

This is normal and it is the reason that a short recoil, modified Browning cam lock action works. It allows the barrel to unlock and the slide to move fully to the rear without hinderance. As the slide comes forward again,the barrel returns to battery and the breech is locked into position with a fresh round stripped from the magazine, ready to fire.

Blowback pistols like the PPK have a fixed position barrel as spring pressure keeps the boltface positioned on the round. High pressure gas from the barrel forces the cartridge case back to operate the bolt. 22s up through 380 cal work this way.