My "smart toaster" recently started tripping the circuit/fuse... Advice please
You have a ground fault, and the GFCI in the receptacle is tripping, as it should, to protect you.

The fault could be anywhere in the wiring of the toaster oven. Since it does not happen immediately, my guess is that it is not in the power switch connection or power supply (the electronic controls have some sort of power supply to convert from high-voltage AC to low-voltage DC) but probably something related to the heating element(s). Possibly a loose connection on one of the heating elements so that as it starts to heat up something shorts and the GFCI trips to prevent any more serious problems.

If the heating elements are designed to be user-replaceable (rare on a small appliance though not impossible) then I would go through the process of disassembly, removal, clean contacts as much as possible on the elements and where they connect in the toaster oven (there may be oxidation or evidence of arcing) and replace the elements. If that doesn't fix it, or if that is not practical, then it is time for a new toaster oven.

Unfortunately, small appliances are not generally designed to be very repairable. Under warranty, depending on the company &amp; the particular device, warranty repair is often:

Do a quick check to make sure it is not a really simple problem and then send out a "refurbished" item which is often just a return from a store for cosmetic or "didn't like it and returned but can't sell it because the packaging is damaged" item.

So a professional repair out-of-warranty is very likely not cost-effective.