@Mossbird
The numbers apply to the potential roll a cat can have when performing their day job. These modifiers only apply to the bottom of the roll, which means every single cat can theoretically roll a 20.
A base value of +0 means the cat can roll a value that is 1-20. The modifiers such as lunch and weather affect the lowest roll, aka that 1.
So.
Our +0 cat on a day with -2 weather and +1 lunch will effectively have a -1 modifier to the job. This makes their potential rolls 0-20.
Cathie with +1 can roll 2-20. On this day with -2 weather and +1 lunch, they will effectively have a range of 1-20.
In your example, Cathie has a +2, making the potential roll 3-20.
Luncheon does NOT touch stats. It applies to the type of job. So +1 Strength isn't to the stat, just to the job that uses Strength as a stat.
Additionally, trinkets don't touch gathering rolls. They alter stats, which can then alter the gathering modifier if the next threshold is reached.