This will be about surge load, or inrush current. Many devices will draw a brief but large current pulse at start up, can be an order of magnitude larger than normal steady current. Enough to weld apparently adequate contacts.
Bigger relay or less load.
As @rossko57 said, it’s about the surge load, not about the normal draw.
Have you seen Apollo 13? There’s an ongoing sequence with Ken Mattingly (Gary Sinise) trying to figure out the right order to turn on the capsule’s systems so that they won’t go over the available amperage in their batteries. He needed to turn on a system to see if it spiked (the surge load) too high, and then make sure there was still enough current to allow for subsequent systems to turn on and spike.
Another example: when I was in high school I was learning to do theatre lighting design and someone told me to turn on a stage light. Unfortunately, I didn’t yet know that it had to be done gradually, so I flipped it right to maximum power and blew out the bulb. I sent too much current too quickly, and the bulb couldn’t handle it.
Since all of your devices are going through the Kasa, when you turn it on they’re all suddenly drawing current at the exact same time…and same as the stage light, all it takes is a moment. That’s why fuses typically blow right when you turn something on, or turn your heater/AC/vacuum/hair dryer to maximum.
Even if devices go directly into a standby state when plugged in (and require you to manually turn them on), they can still draw a lot of initial current.
Why do you have all of those devices going through a single smart plug, anyway?