I am a mechanical engineer so having a worn bush and the rotor rattling around inside would drive me mad. As to urgency it all depends on how badly the mating parts are worn. Judging by all the debris I would recommend you get this cleaned/serviced sooner rather than later.
In the UK a standard service would cost around £200 - £250.
I don’t see any difference between the watches in the two sets of photos, - maybe it’s just the lighting.
In regards to watchmakers I suggest starting a new thread asking for recommendations in your area.
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