So I checked the customization page and found the field where I'm able to add 3 letters airline codes, I guess this is the option you referred to? However I'm not 100% sure how I'm supposed to use it and checking the GSX documentation I couldn't find any info on this topic.
We still haven't updated the manual for it: I thought it was self-explanatory, and there's also a tooltip that helps.
Let's say I always want the Gate Gourmet livery to be used for catering services at all airports. How would I accomplish that?
You can't. The airline codes there will be used ONLY for the ground operators, not the catering operators, which use a different set of codes and there's no way to override them, except editing the SIM.CFG files of the catering vehicles themselves, according to the instructions in the PaintKit documentation, which explain the scoring system.
And same thing for baggage trucks where I would also like to pick some "neutral" livery that will always work without looking strange regardless what airport I'm in and what airlines operate at that airport.
I don't know what you mean with "looking strange". With the override, you can specify the operator YOU want.
If I understand your suggestion correctly I would for example type in SAS for all gates at ESSA meaning the SAS livery would be used but what code should I pick if I want a neutral livery for the catering vehicles such as Gate Gourmet which I don't think has any relation to a specific airline?
As I've said, catering doesn't have anything to do with that code.
And same question how to pick a neutral livery for the baggage vehicles?
You cannot have SOME vehicles a a set in a livery and some in a different one. If you select a ground operator, ALL ground operator vehicles (which does NOT include the catering), will use the same livery.