Electrical – Why does the GFCI periodically trip, especially after a few days’ rain

Sounds like the circuit is sharing a neutral with another circuit.

With your GFCI breaker installed, turn off all other breakers. Reset the GFCI breaker, which should now hold. If it does not hold, then you have a problem with the wiring on that circuit and need to open each box to investigate.

If the GFCI breaker does hold, turn each breaker on one at a time until you find the circuit that trips the GFCI. This is the circuit with a shared neutral.

You then need to open switch boxes, light boxes, on both circuits to figure where the neutrals were wrongly tied together. Suspect anything that looks like a homeowner addition, or fix. A common place this might happen would be in a switch box that controls different lights, with two or more circuits feeding the box. An unknowing DIY-er may have tied all the neutrals together.

Some surge protectors work by "redirecting" surges to the equipment ground, which is pretty much the definition of a ground fault. In this case, it's definitely possible that surge suppressors could be tripping GFCI receptacles/breakers (given a large enough surge).

As for the AFCIs... When electrical contacts separate, they often create an arc between the contacts. This arc spans the gap until the contacts are too far apart, and the arc can no longer be sustained. It's possible (in theory) that the GFCI tripping could create a large enough arc, for long enough to cause the AFCI to trip. It's not likely that a properly functioning GFCI would do this, but if the GFCI was old and worn it could be opening the contacts slow enough that a detectable arc is being produced.

Determining if the GFCI tripping is causing the AFCI to trip, is a simple test. Simply press the test button on the GFCI. If the AFCI trips, you'll have figured out half the problem. If the ACFI does not trip, you could repeat the test using a receptacle tester with a GFCI test function.

If it's determined that the GFCI is causing the AFCI breaker to trip, replacing the GFCI receptacle may resolve that part of the issue.

Figuring out if the surge suppressor is tripping the GFCI, is a more difficult proposition. It will likely require you to monitor the supply voltage over some time, to identify and document possible surges.