How much distance I have to create on a PCB between a coated conductor and an uncoated component pin with a voltage difference of 200V? From different websites and calculators I can only get the information how much distance is needed between two coated conductors or two uncoated pins, but not a mixture of both.
In cases such as this you should probably plan for worst case, which is two uncoated conductors. According to IPC-2221B, with a 200V supply (assuming 200V peak, as in 200V DC or 200V pk AC) you must have a clearance between two uncoated conductors of at least 1.25 millimeters. This is the number I would use for the design, even though you theoretically could get by with a little bit less. This just provides a bit of safety margin, which is especially important because you don't know where the line is between coated and uncoated.
If you don't have enough room for this sort of clearance, I would suggest rearranging your board. I wouldn't trust a clearance of any less, and you really need to make it work, no matter what. Consider running high voltage traces on an internal layer or on the underside.
This is a complex issue that cannot be answered without particulars of the application. At the cleanest environment with the best materials, you'd look at 0.45mm creepage distance. At the worst environment with no coating this goes up to 3.2mm creepage.
Airgap clearance is a fair bit smaller at this voltage, from 0.2mm to 0.8mm depending again on the environment.
The clearances and creepages are defined in e.g. EN 60950 and EN 62368 standards.
Connectors usually define a max working voltage, that's what you can safely use. Higher voltages might be OK but you have to evaluate the case yourself and get it tested before bringing to market. In other words, if you use higher voltage than the manufacturer specifies, you're responsible for it.