Belt pulley is supported by a single large radial clearance large ball bearing that is firmly trapped "
Radially Only" between steel bushings internal to the wheel and axle.
The rear pulley is
separate by design, so it can roll and rock separate from the wheel controlled only by the rubber shock bushings. The more wear on those rubber bushings, the more it can move.
In other words, side to side tilt is OK. Don't sweat it -- it is normal.
Some people replace their rubber bits along the way, others don't.
Some people try to "track" their belts according to the way the rear pulley is when the bike is jacked up, others realise it tracks from one side to the other when decelerating and accelerating (tilt changes according to the load).
Other people just use a 4 1/2" grinder to bevel the sides of the teeth on the belt so it doesn't squeak no matter what it is doing.