The seal on the pump is a potential failure point and will give the symptom you describe.
In an advanced case, the coolant level will drop and the oil level will rise as the coolant drains to the sump, and the oil will discolour as it emulsifies
If you drop the oil into a clean container you might see individual droplets of coolant
Running the engine isn’t a good idea as the oil will be less effective and could cause bottom end damage
The seal isn’t too hard to replace, but it’s a ceramic faced ring and needs great care to avoid chipping it
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