Where is the solarize effect in Final Cut Pro 10.5.1?

The effect might have been in Final Cut Studio (7 or less).

Could you post a screenshot of the effect you're going for?

I think you can just use a Gradient Colorize effect for this.

(This one is free: https://fcpxtemplates.com/gradient-colorize/)

Just switch the color order in the gradient (darks go on the left side, lights on the right). I recommend a 10-25% black on the left and white on the right.

(~15% black)

AFAICT there is no built-in effect called "Solarize".

Is this maybe a third party effect?

You might be able to get close with Stylize->Textures