I’m more of a valve man myself, but this can be very common with SS amps. A sudden voltage drop can cause these pops, and I always get into the habit of bringing the Vol to zero before switching off; SS or valve. It sounds like a capacitor problem, and I have no idea whether your amp has some kind of filter intended to reduce these pops, but your descn suggests there never was one. Given that it’s doing it while you play (have you tried changing your lead, BTW – and make sure your input jack on the guitar is tight), I can only suggest you have a tech look over it.

Sorry I can’t be more helpful than that, but SS amps are not something I have a great knowledge of. Do protect your speakers by zeroing before switching off, though.