My hunch is that your appliances have nothing to do with this. Rather, you have bad wires.
GFCI is not the same as AFCI. They serve very different functions and operate quite differently.
GFCI is for life safety and is conceptually incredibly simple - check to see if hot and neutral have the same current. That's it. Self-testing, indicator lights, etc. are all icing on the cake. But the core is: Compare the current. That can be done with very basic components, which is why it has been available for decades, with gradual increase in required locations as the cost has gone down.
AFCI is for fire safety. It is conceptually, and practically, quite complex. You don't need a microprocessor to figure out GFCI. You can - and modern GFCI (whether breaker or receptacle) uses a microprocessor for self-test and other features, but you don't need it. But AFCI is a much more complex thing, that pretty much requires a microprocessor to analyze the power flow to determine if it is doing "bad things" that would indicate a likely arcing situation that could lead to a fire.
As a result, GFCI is required primarily in wet places - kitchen, bathroom, laundry, outdoors, though recently expanded to include other areas. AFCI, on the other hand, started in the other areas - bedrooms, then living rooms, etc.
Another important difference is that GFCI is primarily a user (wet hands) and device (hot leaking to metal case, or wet stuff touching the user) problem, though it can (with immediate trip every time you use the circuit with any appliance) be due to a wiring problem. On the other hand, with the exception of some motor, compressor, etc. issues (which can affect refrigerators, among things), AFCI is mostly about wires, not about appliances. Which points to an AFCI tripping on every appliance being a wiring problem and not an appliance problem.
There is some overlap now, and it will likely increase over time, depending on NEC version. So you may be required to include AFCI for new circuits in your kitchen. If these are existing circuits, I would recommend installing GFCI (either receptacle or breaker) if you do not already have it (the life safety advantage in a kitchen has been obvious for decades) but not to install AFCI unless required by your jurisdiction.
If you do not already have GFCI (i.e., GFCI/receptacle) then you could install GFCI/receptacle (usually the cheaper method) and get the important safety protection. You could, instead, return that AFCI/breaker and get a comparable GFCI/breaker. If that breaker works fine (I bet it will) then you know that you do not have any ground issues and that your problem with the AFCI is actually arc faults.
That leaves open the question of: Assuming you have arc faults, what should you do about them? If they are real, and not just nuisance trips (e.g., due to heavy machinery somewhere causing noisy power problems in nearby circuits) then replacing those circuits may be a good idea, depending on the age of the wires and the effort required.