[TheDuck]

As you will have seen the OE sprocket has rubber dampers, most replacements don't.
The 0.3mm float that you have seen is fine, it helps with lining up the front and rear sprockets so that the chain runs true.

If there is no float (inwards/outwards movement) on the shaft the chain and sprockets will wear faster on the sideplates/sides of the sprockets. If there is no movement I start to worry!

 

[TheDuck]

I remember the OE item being tight (needed a puller!) but I think this was down to it being stuck rather than anything else. All I can say is that I have ridden many miles with float on the front sprocket ..... the OE rubber is a sound damper and almost certainly allows a bit of float.

Nice bearings :smilebig:

(as a side thought if your wheel bearings are that 'tired' have you checked the dog bone bearings, they generally wear out before the wheel bearings)

 

[TheDuck]

If you find you have lost a socket it is still on the rear spindle :smilebig: