Codes PO300, PO301, PO305

Welcome to 2CarPros. P0300 is random misfire and is likely the result of the other two misfire codes. What did you use for spark plugs? OEM or? There are a lot of fake plugs on the market these days and they can fail rather rapidly. What I would do is swap the plugs to other cylinders and see if the misfire follows them. So put plug no.1 in 2 and no. 5 in 4 and see what it does. If the misfires move then I would source a new set of OEM plugs and install them. Misfires can rapidly destroy the converter because of the raw fuel from those cylinders. If you swap them and the misfires stay in the same places then I would swap the coils in the same way and check the wiring for the coils. The connectors are known to loosen and then you need to replace the connector ends.
But moving the parts first is a quick way to test them without spending money.

It sounds like you have an intermittent issue. If the light stays off you may be okay, I would scan it a few times just to see if there is a pending misfire code. Some codes take more than one cycle to set. A pending code would likely mean you have a loose connection. I don't know if that tool would show live data for misfires on a VW or not, if it did you could see if it shows any misfires while running below the code setting threshold.

Intermittent in that it isn't a constant problem. Something like a loose connector pin on a coil that vibrates just enough to cause a misfire or some dirt in the fuel system that momentarily blocked an injector(s) or more commonly a wire that shorts out once in a while. Any of those could cause those codes, the problem is that finding where the issue becomes much harder if it's not happening all the time. I'd just keep watch on it.

Not as likely as an electrical issue. That's the issue with an intermittent, it could be anything but no way to tell if it only acts up once in a long while. However if the filter hasn't been changed it isn't a bad idea. To change it you need to pull the fuel pump fuse and let the engine shut down as the pressure drops. Then locate the filter back by the fuel tank. The bracket bolt gets removed and the lines get disconnected. Then the new one is installed.

The OEM spec is 4 BAR. The higher pressure shouldn't be used as it will change the fuel flow through the injectors.