How normal are sparks when you plug something in?

As per title.

Normal static cling or predating fireworks?

Into a wall socket (110V)?

Yep. We have a history of power surges.

Plugh the fan, no problem. Plug computer… fireworks.

What’s happening exactly? A small spark between the prongs of the plug and the outlet just as you’re plugging it in?

Sparks? Doesn’t sound normal or safe.
Because of power surges you should get one of those multiple sockets things with a power surge protector for your computer.