Hi @glowworm
Take it on the good side!
Thanks to the overload protection of the tapo plug, which causes it to turn off, you have been saved from much worse possible damage to your home, such as a fire.
It is not a good idea to use these devices with 10A relays for appliances, which as you say consumes 13A at startup.
If they are appliances with linear A/C compressors, these metering plugs are not useful, they measure the Active Power, which for a resistive load, heater, can be valid.
It is best to use contactors, activated by smart switches and magnetic clamp current meters.
It is more expensive and more complex, but much safer.