AFCI/GFCI breaker trips when other breaker turned on

Question

After installing a GFCI/AFCI breaker I turned on breakers individually and flipped breaker below new one and new one popped off.
Same thing on other leg - changed to new and breaker below it caused it to pop when turned on.
If I leave those lower breakers off and turn on new ones they stay on. As soon as I flip old ones on the new ones pop off.

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I changed (CB3 20 amp appliance)with afci/gfci to have counter outlet gfci compliant. No room in outlet for gfci. CB 3 powers fridge and added dishwasher CB5 below it is also 20 amp breaker appliance powers stove, microwave, disposal switched at the other counter outlet. It has the switch for disposal and an outlet. House was built in 1977. I added the dishwasher and disposal. Dishwasher on CB3 and disposal on CB 5

Answer 1

This would typically be symptomatic of replacing a breaker feeding a Multi-Wire Branch Circuit with a single-space AFCI/GFCI, rather than replacing BOTH breakers feeding a MWBC with a two-space AFCI/GFCI.

As soon as you turn on the other half of the MWBC, the neutral current is out of whack and the GFCI trips.

The only way to have a GFCI breaker on a MWBC is to use one double-pole breaker that feeds both halves of the MWBC and therefore can properly sum the neutral current.

Edit to add: This can also happen without an MWBC if the neutrals are merely improperly shared between circuits. It being the next breaker down does suggest MWBC as a distinct possibility, though, and more probable for a house otherwise wired correctly.

Further Edit (with circuit information added to question):

If a house has even one MWBC, 9 times out of 10 it will be the kitchen countertop outlets. The fact that the circuits involved are those makes it all the more likely that this is the case here.

The updated information also states that you added a dishwasher and disposal to the countertop circuits. That is a code violation and needs to be corrected.